Our Gemara on Amud Aleph discusses the idea of making sure that despite someone having been convicted with the death penalty, the mitzvah of “Love thy neighbor” dictates that we choose the least painful and most dignified way to administer the punishment. For example, if the death punishment involves stoning (which actually is preceded by being thrown from a high structure, it should be constructed sufficiently high that he dies quickly, without any unnecessary suffering.”
I will share an unusual application of this principle, from the Shalah (Torah Shebikhsav, Re'eh, Torah Ohr). He says since it is possible that a human may be reincarnated as an animal, the mitzvah of slaughter with a properly sharp knife may also be a fulfillment of this directive. That is, within the soul of this animal, is a human soul, and thus when he is slaughtered properly he finally attains his tikkun or repair. Therefore, this act must be done compassionately.
The mystics attributed a holiness and meaning to everything in the world that is seemingly mundane. Everything is multi-valent, with unknown depth and properties. This elevates the idea of being kind to animals to a different level, but really articulates an approach to the world that all is sacred.