What is the best way to clean a cut on the skin?  i've been told hydrogen peroxide slows cell growth & not to use. What else aside from soap and water

Avoid peroxide. Peroxide not only kills the bad things (bacteria, etc) but also the fibroblasts - cells that promote healing and the production of new tissue. Gentle washing with a mild soap and water is usually adequate, perhaps followed by apply Bacitracin or neosporin ointment. Allowing wound to dry out usually results in prolonged healing and a higher risk of scars.
A gentle cleanser. 2 cups clean water + 1 teaspoon white cooking vinegar. Can be kept in the fridge great for minor scrapes, cuts, even open wounds. Use a clean gauze or cloth soaked in solution and gently clean the wound, continue to soak area with gauze/cloth for 5-10 min. Pat dry & then apply thin layer of vaseline. Do it as often as needed (especially the vaseline). This is also great care for sutured wounds.
Agree but. I would agree with what has been posted. However, I would advise against using Bacitracin or neosporin as these can lead to allergic contact dermatitis. Best thing to apply over the clean wound is either plain petroleum jelly (vaseline) or aquaphor ointment.