I have heard of "blocking" knit goods like sweaters (or pullovers if you like) but trimming saddles I've only heard as "butchering" which sounds cruder than it actually is.
We call it a Stanley knife or mat knife in the US: a box cutter is another beast that uses a single-edge razor blade. The terms are often confused since grocery clerks are handed a Stanley/mat knife on their first day of work and told it's a box-cutter...but it's not.
Measure twice, cut once...you can't put the leather back.