The one I remember was more a square box -- and yes it cut the fabric, then it was torn if it was cotton. Wool was cut with scissors. I remember being taught to order an extra 1/8 yd of cotton so I could trim the edges after the tear. When I was a girl, Mom and Grandma would only let me buy Penny's fabric for clothes -- they felt that all other cotton was too cheap (don't know what brand of fabric, just had to come from Penny's). I was taught to feel the fabric to judge quality , straighten fabric before I started to cut, match the patterns at the seams.
Those machines were great -- you could always be sure how much you got. Guess the newer fabrics did not like being torn -- so sad.