This is going to be another of my longshot questions, as I only remember a few details about the story.
The entire story takes place aboard an interstellar colony ship, and is told from the perspective of the computer running the vessel while the colonists are in suspended animation/frozen/hypersleep (I don't recall the exact term used in the story, but it was pretty some form of the standard suspended animation trope).
For reasons unknown (at first), the computer begins to subject the sleeping passengers to harmful stimuli. I can only recall the first one, which involved the computer tampering somehow with the life support for the sleeping colonists. This action results in a number of deaths, and there is a description of colonists having heart attacks, etc. The deceased colonists are ejected from the ship into space. I believe there are subsequent actions undertaken by the computer, designed to put stress on other areas of their bodies, etc.
The story closes with a twist. Up to this point, the sense is that the computer has malfunctioned, and is randomly murdering colonists for no apparent reason. In the closing paragraph, a rationale is revealed. I'm not sure if the computer is aware of the rationale, or if a curious line in its programming merely reveals it. But the revelation is the word "Mercy." Meaning (at least as I best understood it) hat the computer was giving the colonists who would be too weak, too old, etc. to survive the harshness of the new world they would be colonizing, a death without suffering.
Publication Timeframe/Other Details
Can't tell you much here. I read the story no later than the early 90's, and believe the story to have been fairly old by then. If I had to guess, I'd say 70's or 80's. Might be older than that. I think I read it in a sci-fi magazine, rather than an anthology. I'm afraid I can't narrow it down any more than that.