If two people are on the lease and one person is not paying rent can the other person kick them out?

If your mother and other person signed the lease, then both are jointly and severally liable for the rent. It is a very tricky situation you describe. If your mother agrees to take full responsibility for the lease that may be incentive enough to have the other person move out. An attorney familiar with residential leases may be able to offer a common sense option to offer to the other person.

IF they both are on the same lease, then no, Mom has no right to evict her co-tenant, only the landlord can. Mom can, however, sue the co-tenant for her share of the rent, presumably in small claims court. Mom's other option is to stop paying 100% of the rent and see if she can work out a deal with the landlord. If all the rent is not paid, presumably the landlord will evict one or both of them. If Mom can work a deal with the landlord that she will pay all the rent owed, the landlord may be willing to just evict the co-tenant. Mom cannot force the landlord to go along with this but they may agree. Or perhaps Mom can terminate her lease (is she on a term lease or month to month?) and then sign a new one with the same landlord, minus the roommate, effectively removing the co-tenant's right to be there. Questions? Have Mom talk it over with a local landlord-tenant attorney to see how to best structure the deal. Good luck.

Your mother probably can't kick the deadbeat out as the deadbeat is on the lease. Your mother can sue for 'contribution'. She should see a lawyer about her remedies.