1. To tow someone or something away with a tugboat. In this usage, a noun or pronoun can be used between "tug" and "away." The coastguard ordered for the abandoned freighter to be tugged away. Our propeller got tangled in the vegetation of the marsh, so we had to radio in for someone to come tug us away.
2. To pull or yank (on someone or something) vigorously or repeatedly, especially when doing so has little or no effect. I tugged away at the man's arm, but he wouldn't budge. I've been tugging away for nearly 20 minutes, but it doesn't seem like this thing has moved more than an inch!
tug away (at something)
to pull hard at something; to haul something. She tugged away at the rope, but the anchor would not budge. No matter how much she tugged away, it didn't move.