The topic is somewhat debatable, as all the major powers and players of Europe had a stake in the game of empires. While you await a more substantive reply:

In short, the execution of a monarch was seen as vulgar and shortsighted by those holding sway over his fate. Vulgar, because, while he had been a thorn in Europe's collective side, he had largely acted within the bounds of established international law and codes of conduct for an autocratic leader, as seen by other autocratic leaders. And shortsighted for roughly the same reason; it would set a bad precedent, lest any of these other autocratic leaders or their heirs find themselves, like Bonaparte, at the mercy of their peers in the future.

Further reading from a past instance of this question, by u/LordSariel: https://www.reddit.com/r/AskHistorians/comments/1ra1oe/why_was_napoleon_exiled_and_not_executed/

u/dhmontgomery has a write up here

https://www.reddit.com/r/AskHistorians/comments/kczqdq/why_was_napoleon_exiled_instead_of_executed_even/?utm_medium=android_app&utm_source=share

This answer focuses on the aftermath of Waterloo rather than his first exile though, so I'm sure more can be said!