I'm okay with feeding mice/rats to my animals, except for beardies... since mice (To my knowledge) are an invasive species in Australia which is there for unnatural for a bearded dragon to eat and is also quite hard to digest for them, plus if a beardie were to catch a mouse it would be very rare and the beardie would end up injured if its bigger than a hopper (most likely) unless it got a really good bite on the head before it could attack.
I have two animals that regularly eat mice and rats, a few times I've fed live but for the most part its all frozen thawed (Easier to store and less expensive along with less dangerous). Whenever one doesn't eat its food I can usually give it to the tegu, or even my BTS (Indonesian blue tongue not northern).
Or sometimes my cats...although not really on purpose, when I throw a discarded mouse/rat outside usually one of my cat comes running and gobbles it up either that or one of the foxes living close by eats it. Nothing goes to waste in this house.
Theres a few humane ways to kill a rat/mouse, I've done one way when I was trying to feed a mouse to my tegu but she ended up not wanting it because it was live so I ended up pre-killing it for her. The way I pre-killed it was by dislocating its neck basically... I believe the correct term is cervical dislocation.. if needed I can go into more detail about it but you could easily look it up online. The second way to kill one is by Co2.. which I would have done but I have no idea how to set the gas chamber up and just wanted to get it over with and feed her, but anyway that seems to be the preferred way to kill them as its the least painful way.
I do have to say though, it's interesting watching a snake eat its prey, but not so interesting when your dodging flying pinkie mice parts... if only my tegu realized she didnt need to "kill" everything before eating it. Last time I fed her mice she threw a pinkie at me (Which is basically a baby mouse)... managed to barely get out of the way in time before it hit me in the face.