Martyr is (as a noun)
a person who is killed because of their religious or other beliefs.
or (as a verb)
kill (someone) because of their beliefs.
There is not exactly something like that in our Shastras but to your question is there anything close? i have an answer.
In Sanatana Dharma or Hinduism both Brahmins and cows have eaxltedexalted positions.They are both considered Holy and the holiest among their kinds.
Killing a Brahmin or a cow are both grave sins with the former being listed among the 5 gravest sins(5 Mahapatakas) in all Hindu scriptures.
For example,
Manu Smriti 12.55. The slayer of a Brahmana enters the womb of a dog, a pig, an ass, a camel, a cow, a goat, a sheep, a deer, a bird, a Kandala, and a Pukkasa.
Manu Smriti 9.235. The slayer of a Brahmana, (A twice-born man) who drinks (the spirituous liquor called) Sura, he who steals (the gold of a Brahmana), and he who violates a Guru’s bed, must each and all be considered as men who committed mortal sins (mahapataka).
Now, the same Shastras say that if someone sacrifices one's life while saving a Brahmin or cow commits a great punya(an act of great merit).Similar is the case when that person does not die but saves the cow or the Brahmin.
Manu Smriti 11.79. He who unhesitatingly abandons life for the sake of Brahmanas or of cows, is freed from (the guilt of) the murder of a Brahmana, and (so is he) who saves (the life of) a cow, or of a Brahmana.and (so is he) who saves (the life of) a cow, or of a Brahmana.
The exact verse is found in the Parashara Smriti as well.
I don't know if i have answered your question or not but these are the closest examples i found from Hindu Shastras that talk about "sacrificing life for saving religion,or for the sake of religious beliefs"