cut (something) out of (something)
To remove a shape or figure from something, such as paper, by cutting. The kids are busy cutting paper dolls out of construction paper for a craft project.
cut something out of something
and cut something outto cut a pattern or shape from cloth, paper, sheet metal, etc.; to remove something from something by cutting; to excise something from something. (When both out and of are used, no direct object can intervene.) Sam cut a pig out from the paper. I cut the picture out of a magazine. I cut out the shape of the moon from the paper.