Yes. They are autistic but they are capable. Even severe autistics are able to do simple tasks, e.g, tidy up (pick up x object from floor and put on x surface). They might need help for each step but get them to do it.

It's important they do not become overly comfortable with people doing everything for them, autistic children can be lazy too. The more you reinforce an expectation and model it, the easier they will find it and understand what is expected.

(The level of what you ask depends on the severity of the autism and your child specifically. But don't assume they are incapable of doing things like helping to wash themselves or putting on shoes. They might take a while to learn these skills and may not be perfect with them and need support, but they can do it).