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1.
Verb:

Slang used in the furry fandom to describe masturbation, or the act thereof.

Originates from the slang term jerking off. Comes from that a furry's fursona most likely has "paws" instead of hands, thus the term for pawing.
(Usually used in the same context even if the animal has claws, hands, etc.)

Can be used in past (pawed), present (pawing), or future (paw) tenths.
The red fox sat on the chair, moaning as he was pawing away at his swollen fox knot.
by Anonyfur February 26, 2010
 
2.
Making hands into a fist and rubbing them against another person in a cat-like manner. The act is usually done for attention or to annoy.
Stop pawing me, I'll play cards with you in a minute, neck off necker
by VictorianMan2 September 13, 2009