I had a lump removed in my neck and they cut the nerve. can that cause dizziness

No: Which nerve? The important nerves at risk during a neck dissection or removal of a mass would be the branch of the facial nerve to the lower lip (marginal mandibular nerve), the accessory spinal nerve, which would make your shoulder weak. I suppose it would be possible they could have cut the phrenic nerve, which would cause some shortness of breath. None of these would cause dizziness.