No. With a closed surgical wound, do not rub or scrub the wound.
Every other cleaning step is gentle too. Soak the gauze or cloth in saline or soapy water, and gently dab or wipe the skin. Use a clean, soft washcloth to gently clean your wound with warm water and soap. Wash the area gently with mild soap and water. Clean your wound with gentle soap and water.
Drying is the same. Gently pat it dry with a clean towel. Do not rub it dry. Gently pat dry the area around the wound with a clean towel, and let the wound air dry. Use a clean soft, dry cloth or piece of gauze to carefully pat the wound dry.
The instinct behind scrubbing is that anything you can see should come off, and material does need to be removed. For the skin around an open surgical wound, try to remove all drainage and any dried blood or other matter that may have built up on the skin. But do that by soaking, dabbing and wiping, not by force.
When more than gentle wiping is needed, the answer isn’t harder scrubbing. It’s irrigation, and your provider directs it. Your provider may also ask you to irrigate, or wash out, your wound, filling a syringe with salt water or soapy water and spraying hard enough into the wound to wash away drainage and discharge.
One reassurance if you’re worried by what you see while cleaning: your wound should not bleed much when you are cleaning it, and a small amount of blood is OK. “Much” is the key word. A wound that bleeds more than a little while being cleaned is worth mentioning.