Scabs usually take a few weeks to heal and fall off on their own.
When you cut your skin and you have a scab forming over the cut then it's a good sign that the cut or wound is healing.
The scab forms to protect the cut or wound from infection and as the scab grows new skin will form over the wound or cut.
Then when the cut or wound is fully healed the scab should fall off on it's own.
Sometimes the scab falls off on it's own within a week and sometimes it takes 2 to 3 weeks before the scab falls off.