Just to add to Eliot's answer; to cut across means to travel across or pass over Example : "The caravan had to cut across the desert"

No, they don't. Cut corners = take shortcuts.

'To cut a corner' means 'to cut across' from one road to another instead of following the actual direction of the roads and turning at the junction. So in this sense you could use both because to cut across means 'to go across instead of going around the edge'. 'To cut corners' on the other hand is idiomatic and means to do things in the cheapest, quickest or easiest way.