Unless you want a quilt made from 10" squares you will need to cut them at some time. Quite a few blocks can be made by just placing 2 squares RSF and sewn either side of a line and cut into - HSTs (pinwheels & QSTs), D4P or D9P, 4 patches, probably similar to Turning 20 etc, by sewing lines across but off centre, but they will still need to be cut. You can make stack-n-whack and crazy quilts.
Just my offering of ideas.