How long does it take for cuts on the face to heal?

It depends. If the skin edges are approximated (e.g. Sutures) it takes about a week. If left open to heal, can take longer depending on how wide the cut is. Once initial wound has covered in skin, takes about 6 months for the scars to mature.
4-14 days. Simple cuts and abrasions can take 4-14 days to heal. Wounds that are sutured can take up to a year for scars to settle down. Healing scars should be protected from sun exposure.