I agree with those who have said the "emotion" of dealing with the living can be at least as confronting and difficult as that of dealing with the dead.
While saying that we deal with cases because it's our job is true, I'm not sure it tells the whole story. As an outsider looking in, it's very easy to lose track of the data-gathering and analytical aspects of going to a scene, performing an autopsy, or simply reviewing a report. The more involved you are in the final product -- be it responsibility as a student for answering questions about the case to your attending, as a resident or fellow for answering questions to attendings or sometimes family/police/etc. depending on the case and your supervisors, & preparing reports, or as an attending who is expected to have an answer for everything for everyone -- then the easier I have found it to focus on what I need to figure out rather than getting sidetracked on emotional things.
With the living, I think it's easier to reach a point where you know you can't do anything else EXCEPT get lost in the emotion OR learn to move on to the next patient you CAN help.
In both cases, experience helps. The first few forensic cases I was involved with as a junior medical student, I was somewhat startled at how it affected me -- for me, I could sense a little inner balance tilting back and forth between over-objectifying the process and being weirded out emotionally, until after a few cases I felt comfortable both at the autopsy and after I walked away.
It just so happens that medical school offers much more experience with the living than with the dead -- entire classes devoted to giving patients bad news, convincing a pre-teen to trust you enough to tell you they might be pregnant and what to do when that happens, and treating the terminally ill -- so most students all the way to senior attendings are more comfortable with life, all the way TO but not quite AFTER the end of it.
That's not to say that I don't get emotional about cases, to some extent or other. But, I have a lot more to do than dwell on the parts of the case that would normally make me sad, disgusted, or even angry, were it a personal acquaintance or family member.