The first person the demon core killed, Harry Daghlian, notably allowed the doctors to study and record information about his deterioration due to radiation. I believe Slotin had a similar motivation - that at least, even this slow, painful death could provide valuable information to doctors and scientists.

This was the United States in the mid 1940s, I doubt euthanasia (or even assisted suicide) was much of a thing back then. Plus, as someone else mentioned, there was also the scientifical aspect of being able to study the effects of irradiation.