How do you discipline an Autistic child?

You don't. NEVER punish the Autism. I have an Autistic child myself, and I can tell you from experience that discipline does no good for that reason. What he is doing is probably something he needs to do in regards to his Autism. Removing him from the room is good. How about putting a lock on the door, or doing the laundry when he is not around? If that's not possible, then try the timer trick. Turn a timer on for as long as it takes you to load the washers. Tell him he can't leave whatever area he is in until the timer goes off. As for while they are washing, you might just have to stay by the washer to keep him away. How old is he? I'd have better ideas if I knew. PM me anytime here.

The same way you do with a neurotypical child, but realize it will take longer.

You're not punishing the autism...you're disciplining a child who happens to be autistic. They can and need to be disciplined just as well as the neurotypical.

Make a picture schedule for washing clothes, outlining each step and then post it next to the washer. If he wants to learn how to wash clothes you could teach him.
Or put a large NO (circle with line through it) post on the top of the washer and put a picture of clothes on top of the hamper where he should be putting his clothes. Pictures work wonders with autistic children since they are so visual. But discipline usually doesn't work, depending on at what level he's functioning.

Like you would alter your home for a child in a wheelchair, create an environment with an absolute minimum of 'things he can't do' --sure, you're life will look a little different from your neighbour's, but is looking like your neighbours important enough to punish your child over? Would you hold the same opinion if it were modifications for a wheelchair ... even if none of your neighbours do?

When his environment is set up with his success in mind, very, very little discipline (or punishment) is needed.

My autistic daughter is 22 and have been beating my head against a wall because I have beeen repeating myself over and over about everything.
She will still take clothes out of the washer and throw them on her sisters bed...wet towels she puts in the linen closet.
There is a processing disorder that goes with the Autism and do really process things the same way.They hear but it doesn't "click".
I have never really done anything about her behaviors because she isn't going to understand anyway. I have put up signs though about the things that irritate me.
For instance the bedrooms have independent heating controls. She keeps hers at 70 all day...So I have to have a sign that says to turn heat off during the day. The linen closet gets a new sign every so often.
So my advice is to put up a sign in the laundry saying what not to do and why not ....

I redirect my son. He likes to play with the temperature settings in the refrigerator, and not tell me. Usually, he does this when he's angry with me. I have a book of social stories that covers alot of things that he may face, like when he does things he knows he shouldn't, or how to answer the phone, or other everyday things. I let him read the story to me so that he has a better understanding of what it means. When he was younger, I used pictures to help with the story. If neither of those work, we sit him down and tell him why the behavior is not wanted. Good luck!

As I don't have experience with having an autistic child, I have no other advice other than to tell you that I'm sure there are groups on here for mothers of autistic children. Maybe you should join one, so that you could get advice from other mothers who may better understand what you're going through. Good luck.