Big Slimes divide into tiny slimes that aren't as big as regular ones. So for the Guild's quest, do Big Slimes count as 1 Slime or the x amount of tiny slimes they split into?
I never tried checking on that myself, but if I had to guess, and considering the information on the wiki, I would daresay the big ones count as one. Then any extras to come from the big one also count as one. The erradication goals list slimes of any colour, so I think we could assume that the big ones are just "X colour"
I am fairly certain they count, I dont dwell into the mines as often, though I have killed quite a bunch in the forest. My goal has been steadily progressing regardless. I have never used the slime hutch myself, but I think those also count towards the goal. (the building for slime ranching)
Small Slimes outside the mines count, and small Slimes spawned after killing a Big Slime count, but Big Slimes themselves do not because they are technically a different monster type.
I remember checking on this. Best as I can remember, with v1.2 nothing outside the mines seemed to count. I had specifically made a Slime Hutch to farm them for the goal, and then was really disappointed when I found they weren't counting. The Secret Woods ones didn't count either. Even the ones that come out at night on that one farm map didn't seem to count. Only the ones in the mines. However, now with v1.3, I know for certain that the ones in the Secret Woods count. I haven't built a Slime Hutch yet on this new game with v1.3, but I'm curious to know if they will count now.
Oh really? that does sound awful, I hope the hutch works now! it would be such a waste of a building otherwise!
Secret forest slimes do count as I completed the goal in there once. On a similar note, I do believe big slimes and the small ones that come out are all counted separately. For example if a big slime is killed and three come out, four total slimes were slain. I don't have any information to back this up but one could always confirm or deny it by checking the Adventure's Guild in a morning, without killing any slimes, and matching the total number with all possible slime types tracked on upload.farm EDIT: I did just do that. Big slimes do not count. The small ones do, though.
The slimes in the hutch do not count. Slimes in the Secret Woods do count. I do not know if slime you raise in town count or not.
I think the big slimes doesn't count, instead the small slimes come out of it counts. I never tried it myself, but I think that's how it works.