We now have decades of research on the risk and resiliency factors associated with divorce. One of the primary rules for parents navigating a divorce is the importance of minimizing unnecessary disruptions to children’s lives, relationships, and daily routines. This is important for all children, but it is critically important for kids with special needs, very much including autism.
Specifically, for parents of kids with autism going through a divorce, that means:

1. Be available. At least one parent should be present and available as much as possible. During a divorce, kids need more than ever to have safe, easy, one-on-one time with their parents. 
2. Stay in the same neighbourhood if possible. Being able to play with the same children, visit the same parks, walk the same streets, and go to the same shops, can help children adapt to their new family situation.
3. Change schools only if necessary. School change is stressful for all children. In order to learn and develop positively, children with autism require familiar routines, situations, places, and people. This is always true, but its urgency is heightened at a time of family disruption, like divorce.
4. Keep familiar support systems in place. Change therapeutic teams or approaches only if there are solid reasons showing that (a) the previous system was not working, AND that (b) the new approach will be better.
5. Stay connected with extended family, neighbors, and friends. Grandparents, aunts, uncles, cousins, neighbors, and family friends can be major supportive resources during and following a divorce.
6. Minimize disruptions and changes. Be as dependable and consistent as possible with schedules, routines, and activities.

Although divorce can disrupt a child’s life and development, the basic principles of good parenting hold true. Consistency and routine provide comfort and familiarity, something it’s especially important to remember during times of disruption. As true as this is for every child, it is critically true for kids with special needs, very much including autism.
When parents prioritize their children's needs during divorce--and provide the loving support and consistency the kids need--they ameliorate the inevitable trauma of divorce, and increase the likelihood of optimal outcomes into adulthood.
For more on these ideas:
Targeting Autism: What We Know,  Don’t Know, and Can Do to Help Young Children with Autism Spectrum Disorders, by Shirley Cohen
“Supporting Individuals on the Autism Spectrum Coping with Grief and Loss Through Death or Divorce,” by Marci Wheeler
“Telling Your Kids You’re Getting a Divorce,” by Shelly Allred, Pathfinders for Autism
"Is Divorce Bad for Children?" Hal Arkowitz and Scott O. Lilienfeld