To do something as a means of reducing or eliminating shyness, awkward tension, or unfamiliarity. A variant of the much more common expression, "break the ice." I was so nervous about meeting Samantha's parents for the first time, but her dad immediately told a great joke to cut the ice, and we all got on very well. Everyone was deathly silent after John went ballistic and left the meeting. I tried cutting the ice with a joke, but it didn't help.