Special Education teacher here. If your son attends a school for students with learning differences/medical diagnoses/disabilities, he should have an IEP. If a child needs not only separate classes but a separate BUILDING from non-disabled children, then they certainly require an IEP. I am guessing this must be a private school, one that you are paying for out of pocket. In a best case scenario, your local school district - the one your son would attend if he were in public school - should have identified him as having special needs, written an IEP and placed him wherever the team agreed was the best place for him to learn. If a therapeutic school for students with his difficulties was the best place, it is paid for by the school district.
Even though he isn't attending a public school right now (I assume), you can still write a letter to the superintendent of the public school district where you live requesting he be evaluated for an IEP. They are responsible for his education. Date it and state that you want him evaluated for an IEP specifically in the letter along with a few examples of his behavioral and academic concerns (not completing work is an academic as well as a behavioral concern).
I recommend speaking with an advocate in your area as well, if you Google your community's name and 'special education advocate' you should get some results. Sounds like this situation has been going on a long time and that the school he attends currently is not doing their job. Sadly there are many "private" schools purporting to serve students with autism, but in fact, are scams. A legitimate school of this nature is staffed 100% with special educators and related service providers; it should be a special education SCHOOL, for students whose needs are so severe they literally cannot learn in a typical school environment. If this school is denying your son an IEP it is a near certainty that they fall under the "scam" category. An advocate can help point you in the right direction and will help you interact with them, as well as the public school district.
Just re-read your original post. If his teacher is a "special education teacher" but he doesn't have an IEP, and they are refusing to give him one, you have a very strong case that they KNOW he needs an IEP but are stonewalling the issue. Either that or this teacher is not licensed or certified in Special Education regardless of their claims. Don't let up on them. You are in charge, not them. Are you friendly with other parents at this private school? There MUST be other children experiencing this same treatment.
Sorry you are going through this.