Is it necessary to drain out pus from cut wound?the wound is not deep yet not bleeding, but it stinging when i'm bathing. what should i do?

Get the pus out: Having the pus drain is a good thing. If the pus makes a pocket it gives it a chance to grow and spread. Clearing it is best. Signs of concern would be fever, increased redness, warmth, and pus production. If those occur please see a doctor.

Wound: You need to have this wound looked at by a clinician if you think there is pus (exudate) in the wound.

Infected/inflammed: Red, hot, swollen and pain (stinging) are normal signs of healing and in fact, are integral to healing. If infected and pussy, the wound should not improve, the patient might have fevers, chills, and other systemic signs of infection. Culture of the wound should never be with a swab on the surface but a simple tissue biopsy. Keep it covered with a clean bandage changed every other day till heal.

Basic wound care: In your situation, the stinging when bathing is okay. It is not necessary "to drain out pus", could be dangerous. Okay to wash wound with warm water, a little soap, rinse well, pat dry, hair dryer wound, cover with gauze (available at drugstore over the counter). Check in with doc first thing monday, sooner if spreading redness/fever occurs. If your wound is infected, needs a doc.

Yes, drainage: Draining pus usually indicates an infection or abscess. Wound may need to be reopened, probably antibiotics.