Mines are believed to have suitable cost performance because cheap weapons prevent opponents from freely engaging in activity in mined areas for a comparatively long time. Mine warfare (MW) can be regarded as combat between a minefield planner and mine countermeasure (MCM) forces. The minefield planner equips influence mines with mine counter-countermeasures (MCCMs), which increase the difficulty of their removal. One of the MCCMs is a mine shipcounter, which provides a mine detonation fuse that triggers with some delay after the mine sensor detects vessels. In this paper, we develop a mathematical model of the MCM operation against scattered naval mines with shipcounters and analyze MW as a two-sided warfare game between the minefield planner and the MCM forces. The MCM forces must make a clever choice between mine-hunting or sweeping operations because, depending on the MCM operations, the shipcount has different effects on the removal of mines or on the damage risk to civilian ships transiting in a channel. First, we evaluate the performances of hunting and sweeping considering the mine shipcount; second, we consider a simple game with the minefield planner and the MCM forces as players and analyze rational strategies for these decision makers in MW.