Pastors from many different Christian denominations practice exorcisms.
The Word of God and God, Himself, trump satan and all demons. Note that the Bible says cast out demons, not ask them to leave.
14 And he ordained twelve, that they should be with him, and that he might send them forth to preach,
15 And to have power to heal sicknesses, and to cast out devils:
Mark 3:14-15, KJV
5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not:
6 But go rather to the lost sheep of the house of Israel.
7 And as ye go, preach, saying, The kingdom of heaven is at hand.
8 Heal the sick, cleanse the lepers, raise the dead, cast out devils: freely ye have received, freely give.
Matthew 10:5-8, KJV
17 And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues;
Mark 16:17, KJV
The Apostle's Creed prefix/first line, usually only recited during Baptisms and conformations, is a form of exorcism:
I renounce the devil and all his works and all his ways . . .
Some churches/denominations teach that any believer can perform an exorcism, and others teach only ordained Pastors. It can be extremely intense. Far better that two or more believers (or Pastors) work together for an exorcism/deliverance.
14 And when they were come to the multitude, there came to him a certain man, kneeling down to him, and saying,
15 Lord, have mercy on my son: for he is lunatick, and sore vexed: for ofttimes he falleth into the fire, and oft into the water.
16 And I brought him to thy disciples, and they could not cure him.
17 Then Jesus answered and said, O faithless and perverse generation, how long shall I be with you? how long shall I suffer you? bring him hither to me.
18 And Jesus rebuked the devil; and he departed out of him: and the child was cured from that very hour.
19 Then came the disciples to Jesus apart, and said, Why could not we cast him out?
20 And Jesus said unto them, Because of your unbelief: for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove; and nothing shall be impossible unto you.
21 Howbeit this kind goeth not out but by prayer and fasting.
Matthew 17:15-21, KJV
Some Pastors and others are specially trained for deliverance ministry. Exorcisms are not something that are talked about publicly very often to afford privacy and avoid sensationalism and notariety. Even just talking about deliverance ministry in general can cause unwanted attention or derision among the lost and PC, creating a situation in which the witness could be or is impaired, especially if there have been unsuccessful exorcisms involving people, who are actually demon possessed or oppressed because tends to minimize the public perception of the efficacy of prayer, fasting, The Word, and God.
A real exorcism isn't like the sensationalized events in the movie The Exorcist. However, the movie is based on a real event that transpired in an insane asylum outside the City of Saint Louis. The building is still standing and the part of the building where the exorcism took place is closed off. There is a subterranean tunnel that used to be used to take mentally ill people from Saint Louis to the facility. At that time in history, they didn't have the knowledge and drugs we do today, so some mentally ill people could attract a lot of attention to themselves and those transporting them, and the stigma of having a mentally ill person in the family was far, far worse than it is now, so most such transports were done in the middle of the night in secret to spare the family shame, embarrassment, ostracism, loss of position or employment, etc. The building is no longer a psychiatric facility.
FWIW, some cases of some mental illnesses are demon possession or oppression, rather than mental illness. Sometimes, demon possession or oppression can cause mental illness(es). Sometimes what is thought to be demon possession or oppression is "only" mental illness. Sometimes it can be very difficult to properly diagnose what is actually wrong. Jesus, indeed, is The Great Physician!