I don't have the best extended family. In fact, he has cost me money, been in and out of Jail, threated me and my children, and suffers from a mental disability. The disability is treatable, but instead he treats is via gallons of beer . I"m to the point, I'm ready to "wash my hands of it" It is affecting my family, marriage, and spilling out into my job. My question is, how can you cut someone (a sibling) out of your life? I will always feel guilt over this, and sorrow for him. :(

You could phase him out to the point YOU feel comfortable with.
Like do not call him, do not be the one to initiate anything.
When he calls to ask for anything tell him that you can not help.
If he calls just to communicate use your better judgment.
Do not help him with money and many other things that will enable him to keep on the path he is on. Many people feel guilty and sorry so they give into them only to create more problems. Like my old bf's son was always bailed out of jail by his grandmother and so he never learned his lesson, then he ended up dying because he never learned his lesson.
I see other parents always helping their kids pay bills and buy food because the kids go spending the bill money and food stamps on drugs and then expect everybody else to make up for the money they blew. They never learn and it never stops.

He needs some tough love.

My question is, how can you cut someone (a sibling) out of your life? I will always feel guilt over this, and sorrow for him. :(

First leave the guilt behind you, as there is no guilt in tough love!! Let him know he isn't welcome, until he has gotten help and you can see the benefit. Trying is not good enough! Stick to your guns, no matter any promise he makes, or favors he needs. He must help himself. I wish you luck as I know this isn't easy.

The only thing you OWE a sibling is respect. You don't owe him your money, your sanity, your precious spare time, or accepting a risk to your family/career. You don't.

But you owe him respect. Respect his choices and his right to make them. IF he chooses not to treat his disability or to be drunk, that's his business. Now, respect him enough to leave him alone... out of respect.

If he ever asks why you're not contacting, helping, whatever... answer him politely and respectfully like you would any stranger. "I am not involved with people who make the choices you make in any sort of ongoing way. But I respect your right to live how you want and not feel judged by me. If you are around me I will have no choice but to come down on you about your lifestyle...and honestly I don't have the energy for it and you don't need the grief from me. Please enjoy your life the way you want. I can't be around it, though, so it's best we just leave things be. Okay?"

He won't change, not from anything you do AT him, but he might change on his own because of the things HE does and what it COSTS him. Effectively losing you in his life may be just the ticket. But it has to be a REAL event for it to be effective.