I am wanting to evict the other person listed on our lease. First off, when he signed the lease with me 17 months ago, on the day we were supposed to move in, he decided not to move in, so it was just me, and since, with the landlord knowing and being OK with, my boyfriend has moved in, although a new lease was not drawn up. 8 months ago, the other person on the lease decided to move in and due to him being on the lease, I let him. Ever since, there has been tension and problems. The "other person" is claiming accusations that are not true. The landlord wants them to move out, but has no specific reason to give them the notice, and said that I could, but I am having a hard time finding the resources to get this done. There is no specific reason to evict him other than he is mentally unstable, has been in the mental hospital, as well as he has not lived here in the past 3 weeks, but keeps his belongings here. He has never done any house or yard work, and taken over most of the house since he has been here. I have told him I did not want him here, and the past 2 months he says he is going to move and nothing has become of it. He now wants me to get my boyfriend to move out because he has some issue with him. I am tired to playing his games and do not trust what he may do. I have a lot to lose and do not know how to deal with it.

I believe that there is another post on here similar to yours and it was suggested that the Landlord do the evicting as it's not up to you (the tenant) to do so. Evictions can be done if there has been complaints received, so the landlord would be within his/her rights.
Here is the link for another post similar to yours.
https://www.askmehelpdesk.com/real-estate-law/desperate-evict-roommate-who-lease-395338.html

Talk to the lanslord... if you HAD a 12 month lease, it is now month to month. You can get a new lease drawn up in your name only... and have the landlord give them their required notice to vacate that the current month to month lease (that they are on based on the original lease) will not be extended.

Exactly where do you live because tenant and landlord rights do vary considerably from city to city or state to state.

In many locations the landlord doesn't NEED a reason to terminate a month to month lease. Only have to abidle by the required notice the local laws allow.

I would also consider giving them an option to move out... and get this in writing and signed by them, or take them to court for their portion of the rent they have not paid from day one of the lease. Their name was on the lease... they had the obligation to pay it.

Its not an eviction per-say... but an enticement to leave voluntarily. Once they do get a new lease in your name only and as such they have zero rights of return. AND has to remove their property.

Now if they still refuse to go or pay... the landlord can have them removed from the prioperty (in most places). Again it would help to know what city and state so the actual laws that pertain to your case can be referenced.