Pro-Russia rebels in eastern Ukraine saw some of their worst battlefield setbacks in weeks Monday as the West agreed on tougher sanctions aimed at forcing Moscow to cut support for the militias—posing fresh challenges on two fronts for Russian President Vladimir Putin.

Ukrainian forces were advancing from the north and south in an effort to cut off Donetsk, one of two remaining separatist strongholds, from fellow rebels in the other, Luhansk, as well as their supply lines to the Russian border, officials on both sides of...