There is three people on my lease, my daughter, me and a male roommate. Either me and my daughter or the roommate needs to leave because I am tired of the fighting between myself and HIM. He went to remove himself off the lease and I am my daughter were going to remain. The office told him if he does that then his wages would be garnished even though I am still here and would be held responsible for the rent. Is it legal for them to receive rent from someone after they receive full rent?

No, his wages can't be garnished unless they first sue him and get a judgment.

And they can't sue him unless he has breached the lease.

There will be no breach of the lease if you continue to pay the rent.
The person at the office was merely trying to warn him of the potential consequences, should you not make the rental payments.

A lot depends on how the lease is written. But there is no way they can garnish his wages without a court order. And I don't see how they can get a court order unless they are being damaged.