I've generally interpreted it in two different ways, neither of which is this accepted version (though I would not contest that the title must've originated as described in this article).
First, as in reference to gardening, where a blade may be run along a stem to remove undesired branches or buds. [MINOR SPOILER[?]]This especially fits with the "tree" motif that features through the second film.[/SPOILER]
Secondly, as a roundabout reference to Ockham's Razor, in that Blade Runners have a responsibility to make sure that the "official explanation" (most likely to be believed) for something is the "simplest possible" explanation for something - i.e., they cover up what is a complex situation for the public by eliminating the source of moral or ethical complexity (specifically, by "retiring" replicants).
First, as in reference to gardening, where a blade may be run along a stem to remove undesired branches or buds. [MINOR SPOILER[?]]This especially fits with the "tree" motif that features through the second film.[/SPOILER]
Secondly, as a roundabout reference to Ockham's Razor, in that Blade Runners have a responsibility to make sure that the "official explanation" (most likely to be believed) for something is the "simplest possible" explanation for something - i.e., they cover up what is a complex situation for the public by eliminating the source of moral or ethical complexity (specifically, by "retiring" replicants).