One may not crossbreed two species of animals, as we read, “You shall not let your livestock mate with a different kind (kilayim)” (Leviticus 19:19). However, it is permitted to have different species in one enclosure. Should they choose to mate, they do not have to be separated. This prohibition applies in Israel and the diaspora, and some say it applies to the animals of non-Jews as well. While it applies to mating two different species, two breeds of the same species may be crossbred. If someone transgressed and crossbred two species, one may use the animal born as a result. One of the most famous crossbreeds is the mule, the progeny of a donkey and a horse.
The Torah also forbids working different species of animals together. For example, one may not have an ox and donkey plow together or a horse and donkey pull a carriage together. As we read, “You shall not plow with an ox and a donkey together” (Deuteronomy 22:10). This mitzva may also be meant to teach us to be merciful towards animals, as having two different animals working together causes them to suffer.