Don't worry, this type of cut does not hurt. Doesn't even require a bandage.
The cut of clothing refers to the way the garment hangs on the body based on the shape of the fabric pieces used to construct it, the position of the fabric's grain line, etc.
Cut in clothing, sewing and tailoring, is the style or shape of a garment as opposed to its fabric or trimmings.
In regard to dresses, you will find various dress cut terms.
In summary, the cut of clothing is the style of clothing. It does NOT mean your clothing is torn or ripped. If you want clothing with cuts in the fabric, Learn about ripped jeans.
By the way, if you want to learn about "cutting", you may want to learn about pinking shears.