If he has had no behavioral or emotional problems outside of school since your divorce, he may unconsciously be using school as the one place to vent the anger, frustration, and sadness caused by your divorce. Many kids of divorce try to behave like angels with their divorced parents, hoping that they can bring them back together again, while using school as the place where they can release all their negative feelings of anger, fear and anxiety.
I would be most surprised if your son is not suffering some inner turmoil, since you state that you and his father have "not been getting along too well." Even when divorcing parents behave as lovingly as possible with each other, the children always undergo emotional upheavals. An eight-year-old does not have the ability to respond in a sophisticated emotional manner to the jarring upheaval of a divorce. He is probably confused and scared about his life right now.
Please ask both his teacher and his guidance counselor to discuss their observations and explanations of his school behavior with you, if you have not already done so. It sounds like you and his dad may not have been able to maintain a civil, united front for him as a couple. Your focus needs to be on the emotional health of your son. Ideally, you and his dad should get some counseling from a therapist who has worked extensively with families of divorce.
If your son's teacher, guidance counselor, you, and his dad have not been able to understand his school misbehavior, then maybe he is showing you a giant red flag, screaming to you that he can't control himself. Don't let your boy continue to hurt so badly. Get him some professional help from a therapist who treats children of divorce who are in his age group. He needs a safe, caring place where he can let someone see his pain, so that he may receive the help that he desperately needs to begin coping and healing from your divorce.
Perhaps you and his dad can come to agree that his well-being is your top priority now and that your energy and love should begin to flow, as a couple, in that direction. Don't count on the passage of time to heal your son. You need to take action now.