What The Bible says about Mental illness

The Bible doesn't have much to say about mental illness, although there were a few people in the Bible who seemed to be afflicted with it.

King Saul

Saul's madness was caused by an evil spirt from the Lord.

But the Spirit of the LORD departed from Saul, and an evil spirit from the LORD troubled him. 1 Samuel 16:14

The evil spirit from God came upon Saul, and he prophesied. 1 Samuel 18:10

Later the spirit of God came upon him and he stripped off his clothes and prophesied naked all day and night.

And the Spirit of God was upon him [Saul] also, and he went on, and prophesied ... And he stripped off his clothes also, and prophesied before Samuel in like manner, and lay down naked all that day and all that night. 1 Samuel 19:23-24

King David

David faked madness to get out of trouble.

He [David] feigned himself mad in their hands, and scrabbled on the doors of the gate, and let his spittle fall down upon his beard. 1 Samuel 21:12

Jesus

But the most famous person who was accused of insanity was Jesus.

His family ("friends" in the KJV [1]) thought he was mentally ill.

His friends ... went out to lay hold on him: for they said, He is beside himself. Mark 3:21

And many of the Jews thought he was mad and possessed by a devil.

There was a division therefore again among the Jews for these sayings. And many of them said, He hath a devil, and is mad. John 10:19-20

Causes of mental illness

According to the Bible, there are only two causes of mental illness: God and demons (devils, evil spirits, unclean spirits, etc.).

Sometimes mental illness comes directly from God.

If thou wilt not hearken unto the voice of the LORD thy God, to observe to do all his commandments ... The LORD shall smite thee with madness. Deuteronomy 28:15-28

So that thou shalt be mad for the sight of thine eyes which thou shalt see. Deuteronomy 28:34

Take the wine cup of this fury at my hand, and cause all the nations, to whom I send thee, to drink it. And they shall drink, and be moved, and be mad. Jeremiah 25:15-17

In that day, saith the LORD, I will smite every horse with astonishment, and his rider with madness. Zechariah 12:4

Sometimes mental illness is caused by devils.

When Jesus cast out devils from a wild, naked, homeless man (by sending them into a herd of pigs, which ran off a cliff, fell into a lake and drowned), the man put his clothes and returned to his "right mind."

And they arrived at the country of the Gadarenes ... there met him out of the city a certain man, which had devils long time, and ware no clothes, neither abode in any house, but in the tombs. And they besought him [Jesus] that he would not command them to go out into the deep. ... And he suffered them. Then went the devils out of the man, and entered into the swine: and the herd ran violently down a steep place into the lake, and were choked. ... Then they went out to see what was done; and came to Jesus, and found the man, out of whom the devils were departed, sitting at the feet of Jesus, clothed, and in his right mind. Luke 8:26-35, Cf. Mark 5:1-, Mark 5:1-20

The biblical treatment for mental illness depends upon whether it comes from God or from demons.

If it comes from God, it can sometimes be managed with harp music.

Saul's madness seemed to go away, at least temporarily, when David played his harp.

When the evil spirit from God was upon Saul, that David took an harp, and played with his hand: so Saul was refreshed, and was well, and the evil spirit departed from him. 1 Samuel 16:15-16

When it's caused by demons, try sending them into a herd of pigs, like Jesus did with the Gadarene demoniac.

Although the Greek word in verse 3:21 could refer to either family or friends, it seems more likely to be family, since verses 31-35 clearly say that Jesus's family were asking to speak to him, where Jesus denies that they are his family, saying that his true family are his followers.
For more on this see Rabbi Tovia Singer's explanation in this youtube video.