A cutoff is a new line that ‘cuts off’ from the existing main for some purpose, usually rejoining it at some further point. This might be done to shorten a convoluted route using better modern grading techniques, as in Truesdale’s cutoffs, or to lower peak compensated grades, as in the Morrisville cutoff [note: all the fun started across the river from Trenton…], the Atglen & Susquehanna, etc. on PRR. (Note that this is slightly but significantly different from cutting off distance or cutting down grades, which is not always what happens…)
There is a slight semantic difference between a ‘cutoff’ and a whole new main line, like the proposed Sam Rea Line to bypass Pittsburgh, and the west-end connection of it into Ohio. Arguably the same would exist on the east end of it, which would bypass Philadelphia and probably Trenton to connect more directly to the New York market. But in a sense these could be considered ‘cutoffs’ too… just replacing rather than improving a route. In a sense this was true of the Lackawanna Cutoff as it so thoroughly replaced parts of the Old Main Line that they were regraded for highways.