NOVO-OZERNE, Ukraine—Its escape to the open seas blocked by sunken ships, the Ukrainian minesweeper Cherkassy weaved and lurched in a narrow gulf on Tuesday afternoon with a symbolic, if inevitably brief, distinction: the last Ukrainian military vessel in Crimea not yet seized by the Russian navy.

From the banks of the gulf cutting into the western flank of the peninsula from the Black Sea, the Russians watched the trapped, constantly moving ship, then dispatched patrol boats to chase and bump the stubborn vessel in several...