Does Exiling a Creature Kill It?

no, cards that are exiled instead of going to the gy and "dying" do not trigger abilities off other creatures dying, like say Blood Artist.

Does exiling a creature count as dying?

If the creature goes to the graveyard and then moves to exile, then it counts as dying. However, if it goes to exile instead of the graveyard, then it does not count as dying. If a creature dealt damage this way would die this turn, exile it instead. If an event is replaced, it never happens.

What does exiling do in MTG?

To exile an object is to put it into the exile zone from whatever zone it's currently in. An exiled card is a card that's been put into the exile zone. 406.3. ... Cards “exiled face down” can't be examined by any player except when instructions allow it.