She gave the rope a sharp tug.

Literal

She [topic-は] that rope [object-を] sharply pulled.

ぐいっと is a 擬態語 (state mimetic) for a sharp, vigorous motion — typically a quick pull, jerk, or yank. The small っ inside builds in the percussive feel: a momentary tightening before the tug. Closely related ぐっと expresses similar force but with more sustained pressure (think of a tight hold rather than a quick yank). 引っ張る ('to pull, drag, tug') with ぐいっと paints a vivid one-action picture of a single decisive pull — the kind of mimetic-plus-verb pairing that makes Japanese description feel cinematic.