A long time ago, when dinosaurs ruled the earth ...
All right, not quite that long ago, but for the first few novels my ambitious childhood self wrote, when I started a new draft, I had my printout in my lap ... and I typed, from the beginning, in a brand-new file. Sometimes, I would transcribe verbatim; other times, I would change, add or omit. The act of re-typing it forced me to consider everything I was writing. And it worked well enough - I might go back to it some day - but it was tedious and time consuming.
After that, I moved to editing in-line. However, I started finding that I wasn't making enough changes: I was reluctant to remove things because they would be gone forever. I'd also occasionally have problems with cutting something and later realizing I shouldn't have ... and at that point, I wouldn't have any options for fixing it.
So I started the technique that I use now for novels and certain short stories requiring significant rework: every time I start a new draft / editing pass, I save a new version of the file. On a practical level, this allows me to go back if I need to reverse a cut; I can also double-check for consistency between versions. On a psychological level - probably just as important - I feel more comfortable slashing even large chunks of manuscript. They still exist: I haven't destroyed the words forever.
I don't so much kill my darlings as lock them up in a psychiatric ward.