cut away
1. To cut two things apart. A noun or pronoun can be used between "cut" and "away." I think that cutting away this part of the bush will bring more light into the house.
2. In film, TV, or video editing, to interrupt a sequence by showing something else, typically something related to the main sequence. My favorite part in this scene is when it cuts away to the shadow on the wall—it's so eerie!
cut something away (from something)
to separate something from something by cutting. The doctor cut the wart away from the patient's foot. She cut away the loose thread.