Does the Church still heal the sick and raise the dead?

Perhaps you've heard an atheist or skeptical challenge to the effect of, "If the Church really was divine, why doesn't it heal the sick and raise the dead, etc., like it says in the Bible:

And these signs will accompany those who believe: in my name they will cast out demons; they will speak in new tongues; they will pick up serpents, and if they drink any deadly thing, it will not hurt them; they will lay their hands on the sick, and they will recover. (Mark 16:17-18)

The response to this is twofold.

LITERAL
First, this prophecy was fulfilled in the immediate early Church following the Ascension. Most of the promises are recorded to have occurred in the book of Acts. As well, there have been other records of such miracles occurring in the subsequent history of the Church.

• The matter of exorcism is attested, for example, in Acts 16:18. In Church history, the ministry of casting out demons in exorcism is attested by a number of other subjects and witnesses.  This is the case even today with lay people and clergy who work in close conjunction with medical professionals in order to rule out medical conditions. See the footnotes for references.
• Regarding the gift of tongues, the Scripture attests to the phenomenon in the book of Acts, which followed Christ's promise. Some early Christian texts repeat the claim (e.g. St. Irenaeus, Against Heresies, 5.6.1). It is sometimes attested in modern times that this gift, perhaps, is now rare or non-existent (e.g. Fr. Edward O'Connor, The Catholic pentecostal movement, 1971). Read further in the next section regarding a concentration of miracles in the early Church.
• The matter of handling serpents or poison, again, is attested in Acts. Paul is bitten, yet unaffected, by poisonous snakes (Acts 28:3-5). In Church history, one of the miracles attributed to St. Edith Stein (aka St. Benedicta of the Cross) is the recovery of Benedicta McCarthy who in 1987 ingested "19 times the lethal dose of acetaminophen" and recovered instantly.
• Healing the sick is attested in Acts 3:1-10, Acts 14:8-10, et al. Peter is recorded to have raised the dead in Acts 9:32-42. Of course, there have been numerous healing miracles attributed in every age of the Church, such as the aforementioned Edith Stein miracle, and even more recent miracles, such as attributed to Bl. Fulton Sheen.

St. Peter Raises Tabitha, Fabrizio Santafede, 1611, acquired from Wikimedia Commons

For the purpose of interacting with a skeptic, it is enough to note that the Biblical text records fulfillment of Christ's prophecy. Whether the skeptic believes the miracles is a different matter. The text of Acts accounts for the prophecy in Mark.

SPIRITUAL
Secondly, and more importantly, the Scriptural promise must be understood spiritually. After all, Scripture likewise alerts us, "And do not fear those who kill the body but cannot kill the soul; rather fear him who can destroy both soul and body in hell." (Matt. 10:28)

Preservation of the soul, in the order of Christianity, is more important than preserving the body. That, of course, does not suggest we are to neglect the body, because the body is also the sacred temple of the Spirit (1 Cor. 6:19).

But, Scripture often uses the figure of healing the body as the figure of man healed of sin. The opening of the Mark 16 prophecies fits with this healing language, which is indicative of healing sin.

Consider another occasion on which Christ juxtaposed the healing of a body in order to make a point about spiritual healing. After healing the paralytic whom was lowered through the ceiling, Christ said,

But that you may know that the Son of man has authority on earth to forgive sins." He then said to the paralytic, "Rise, take up your bed and go home." (Matt. 9:6)

Christ reveals the purpose of performing the visible healing—that the onlooker would understand that healing of sin is real, even though he cannot see it. Christ performed a visible healing in order to give cause for his audience to believe the invisible healing. They saw the paralyzed man healed. They had reason to believe the invisible, but real, wounds of sin were likewise healed by the power of Christ.

Luke quotes Christ analogizing sin and sickness. When asked why he would engage sinners, Christ replied, "Those who are well have no need of a physician, but those who are sick." (Luke 5:31)

The Catechism echoes this sentiment in multiple places. For example:

• [W]e are dead or at least wounded through sin... (CCC#734)
• Thus the sinner is healed and re-established in ecclesial communion. (CCC#1448)
• But [Christ] did not heal all the sick. His healings were signs of the coming of the Kingdom of God. They announced a more radical healing: the victory over sin and death through his Passover. (CCC#1505)

Return now to the Mark 16 prophecies and the spiritual meaning becomes clear. This spiritual understanding is explained by Pope St. Gregory I (d.604):

Are we then without faith because we cannot do these signs? Nay, but these things were necessary in the beginning of the Church, for the faith of believers was to be nourished by miracles, that it might increase. Thus we also, when we plant groves, strong in the earth; but when once they have firmly fixed their roots, we leave off irrigating them. These signs and miracles have other things which we ought to consider more minutely. For Holy Church does every day in spirit what then the Apostles did in body; for when her Priests by the grace of exorcism lay their hands on believers, and forbid the evil spirits to dwell in their minds, what do they, but cast out devils? And the faithful who have left earthly words, and whose tongues sound forth the Holy Mysteries, speak a new language; they who by their good warnings take away evil from the hearts of others, take up serpents; and when they are hearing words of pestilent persuasion, without being at all drawn aside to evil doing, they drink a deadly thing, but it will never hurt them; whenever they see their neighbours growing weak in good works, and by their good example strengthen their life, they lay their hands on the sick, that they may recover. And all these miracles are greater in proportion as they are spiritual, and by them souls and not bodies are raised. (Pope St. Gregory I, commentary on Mark 16, quoted in St. Thomas Aquinas's Catena Aurea)

It is worth emphasizing that St. Gregory also expounds on why the volume of miracles are more prevalent in the early Church—because they were useful in giving the Church root. From there, the Church stood with greater strength, having a firm foundation and the assurance of a divine pedigree. The Catechism #156 refers to miracles as one of the means by which faith is nourished (cf. Is faith belief without evidence?). Although miracles have occurred in every age in the Church, it is sensible to expect greater "proofs" would be given at the beginning of a new era in the divine economy of salvation. This is somewhat analogous to an infant requiring much sleep until he grows in strength and depends less on it.

St. Gregory's spiritual interpretation of the Mark 16 passage is echoed by others, including Fr. Cornelius Lapide (d.1637), the Flemish exegete, by quoting St. Bernard (d.1153):

Mystically: S. Bernard (Serm. de Ascens.) says, “The first work of faith which worketh by love is compunction of heart, by which, without doubt, devils are cast out when sins are rooted out of the heart. After that they who believe in Christ speak with new tongues when old things depart but of their mouth, and for the time to come they speak not with the old tongue of our first parents, who declined unto words of wickedness in making excuses for their sins. But when by compunction of the heart, and confession of the mouth, the former sins have been blotted out, in order that men may not backslide, and their latter end be worse than the beginning, it is needful that they take away serpents, that is, extinguish poisonous suggestions, &c. If they shall drink any deadly thing it shall not hurt them. This is, when they feel the stings of concupiscence, they shall not consent. They shall lay their hands upon the sick, and they shall recover. This is, they shall cover their evil affections by good works, and by this medicine they shall be healed.” (Lapide, Commentary on Mark 16)

So, when someone asks, for example, why doesn't the Church still heal the sick or raise the dead, the answer should be that it does, every day, in the sacrament of Confession. Whenever an earnest soul makes his sacramental confession, a miracle occurs. We have the visible installment of belief from the miracles of Christ and his apostles and saints through the ages. It is up to us to recognize the greater healings occurring in spirit.

Further resources:
Christ’s Power Shines Even in “Creepiest” Exorcism Case, Says Psychiatrist by Patti Armstrong, 2018.
The Rite by Matt Baglio, 2010.
Hauntings, Possessions, and Exorcisms, Adam Blai interviewed by Patrick Coffin, 2019.
US exorcists: Demonic activity is on the rise by Patti Armstrong, 2011.