No. Wash it well with clean water, check if the wound is wide open. If so, have someone drive you to the hospital to get it stitched.
If you have trouble moving or feeling your fingers, have that checked out asap.
Keep the wound exposed to air for as much as is convenient, if not bleeding like crazy. Keep the hand closed slightly closed to give it a chance to heal fast and without scar tissue.
My qualifications are those of an amateur carpenter.