Used for plants and animals, including pets. 雑種の犬 is a common way to say 'mixed-breed dog'. Can sound slightly informal or colloquial when applied to dogs, but is neutral in biological contexts.
Our dog is a mixed breed.
This plant is a hybrid and resistant to disease.
雑種 refers to a mixed-breed animal or plant, whereas 混血 is used specifically for people of mixed parentage and would sound odd or derogatory applied to a human.
Compound of 雑 (ざつ, 'miscellaneous, mixed') and 種 (しゅ, 'species, breed'). The reading ざっしゅ results from assimilation of つ to っ before し.