Does the gastroentrology doctor remove bowel impaction?

Sometimes. Gastroenterologists can endoscopically remove food impactions of the esophagus using an endoscope. Stool impactions in the colon can be removed by any type of doctor, usually manually (using a finger/hand) in combination with laxatives or enemas. Rarely a gastroenterologist can assist with a colonoscope, but it is rarely necessary.
FECAL IMPACTION. Do you mean 'fecal impaction' due to chronic constipation? If so, your primary care doctor will be enough to advise and treat you. If something more than this, s/he may refer you to a gastroentorologist. If bowel obstruction, your primary care doctor will refer you to a surgeon. Is this you wanted to know?