Dark_Ildar, kill them if they run away. In multiplayer maps, there are no scripted dialogues to "do evil deeds" or "do good deeds," so you get more points for monsters. If they don't run away, you don't get any points. And in both the campaign and multiplayer, you can get Blood or Tear points in libraries or arenas.
Here's an example:
I'm playing as demons, it's the 2nd week already, and I have Devastators (or something like that). When I attack the Shark Guards, they run away. I attack without fear, and after the battle, when I check the hero's window, I don't notice any increase in Blood points, and it's the same in all battles...