Cutting can be a way of disconnecting from emotions, while crying is an overflow of emotions. I don't remember cutting and crying at the same time. I have cut in order to stuff back the emotions and get them under control so that I could function (like when I cut after my husband had yelled at me and my daughter, shoved me, and thrown the couch across the room, and I didn't have time to deal with the feelings because I had to go to work and be functional. I cut instead.) When I was really severely depressed, I didn't cut. Those were the times when I let emotions overwhelm me. I've been sad sometimes recently, and have cried a few times, and have not cut.

Maybe you are onto something there. It doesn't seem that cutting and crying often go together.