Theoretically, only a violation of the Laws of Magic by a mortal practicioner would warrant a formal execution. And in practice, given the number of people involved, this is probably followed reasonably closely.
Now, as far as just killing someone (or thing); the Wardens have a LOT of latitude. Wardens are supposed to be trained carefully to avoid abuses of power; but given Harry's former teacher, accidents happen. So, basically, as long as a Warden's actions are against beings that can't file formal protests with the White Council, a Warden can kill pretty much anyone they want without much worry.
Most Wardens probably don't abuse this power. Most of the time. Most of them. But consider
Luccio's surprise when told by Harry how Morgan had been looking for excuses to execute him
; quis custodes ipsos custodes, after all. There are few Wardens, a lot of territory, and little oversight. Given that Wizards are human, it would be more surprising if no Warden had ever abused their position and authority, ever.
I'd suspect that a lot of abuses are small things; cadging free drinks, discounts on books of lore, that sort of thing. But as the books show, it can become a lot more serious.
So, actually, you could get marked for death by a Warden just by annoying them sufficiently and not having enough connections to make your death problematic politically.