The phrase "cut shorter" is correct and can be used in written English.
It means to make something smaller or shorter in length. Example: "I had to cut my speech shorter because I ran out of time."
This will fit an adult's head so cut shorter strips for a child.
The field will be bigger and wider and the grass will be cut shorter and better watered.
Her hair, cut shorter this summer so she could be in and out of the lake at the Lutheran camp, bounced, releasing a scent of shampoo.
The answer to Christa's problem is simple: it's time to grow up, get your hair cut shorter, and kick the miniskirts into the back of the cupboard.
I remember one woman in particular, who hung onto her girly cotton frocks for several years too long and then one day turned up with her hair cut shorter, wearing something well-cut and flattering.
Hair was first cut shorter by trendsetters even before the war, and by the 1920s the shingle and the more severe Eton crop were being adopted by many women.
