From my experience as an abuse survivor, and having worked with many other survivors over the years, yes it's common to cut off emotion. It's a coping mechanism - pretty much the only one a powerless child has. It then becomes a habit.
It can feel like your absence of emotion is keeping you safe, because the thought of actually experiencing our pain, fear, rage, shame is literally unbearable. This is especially true for those of us who were also taught or shown as children that expressing negative emotions was forbidden or shameful.
However, we cannot suppress our pain without a cost. We can't let go of that pain until we've accepted it and let that little child inside us express that pain and sorrow. That child needs to be heard; that child needs to hear that they are safe and loved and did not deserve the abuse.
It is a hard, hard journey. But it can be the most worthwhile work of your life.
I felt, for me, I owed the little Furiosa inside me a debt. She protected herself by freezing, trusting the cold to numb her physically and emotionally in order that she could survive. She kept her silence because she knew that speaking her truth would mean more pain. She made that sacrifice so that I could live. I repaid that debt by giving her a voice and a safe place to be heard. Now that she knows she is safe, she has let go of that pain - and that means I am no longer making choices which are driven by that pain or the damaging beliefs that resulted from the abuse.
I hope you can find a path to peace, OP. You deserve to be happy and whole. So do we all 💐