'Skip', like most short words in English, has lots of meanings. The most common similar meaning is used to convey moving in a direction with a bounce (the children were skipping down the sidewalk). Without 'rope', that would be the default meaning of 'skip'. And as Eric said, in the US we typically say 'jump' but in that case too you need to specify that you are 'jumping rope' (neither 'jumping', nor 'jumping with a rope')
By the way 'skipping with a rope' sounds awkward to my American ear. Maybe it's British, or maybe there's some other kind of fitness 'skipping' that I don't know about.