This is an odd question with some odd facts. While it’s true that many homeless people have a mental illness, it’s not always the mental illness that made them homeless. Sometimes there just isn’t enough community and government support for those with mental illnesses, and that leaves these people subject to whatever hand the fickle finger of fate deals them.
As for those with autism, not many people with autism are homeless. The reason for this is that autism was once considered very rare, so anyone who’s old enough to be homeless probably has never been diagnosed with ASD. If there are any homeless people with ASD, the government has no idea who or how many because the homeless are often adrift in the wind and nothing about them is recorded. Shelter operators who have a clue or two about ASD might notice that one or two of their nightly guests could very well be autistic, but since the homeless rarely seek out psychological help of any kind and are fortunate when they get medical treatment, it’s not likely that anyone on the street will ever be diagnosed and recorded as having autism.
On the flip side, people with autism can end up on the street, just like everyone else. It doesn’t happen much, because those that are diagnosed with ASD have families who support them and who have turned the world on its edge to see that they are in a safe place and all their needs are met. The high functioning ones often have spouses and children of their own, and it’s only uncontrolled impulsivity that can put them out on the street. (E.g., gambling, stealing, living beyond one’s means by buying too much or too many things, etc.)