The moves open up $13.05 million in salary cap space, according to Over The Cap.
Both veterans spent two seasons with the Giants.
Ogletree contributed 173 tackles, two sacks, and six interceptions during his tenure. The 28-year-old was acquired from the Los Angeles Rams via trade. He had two years left on his contract.
Martin appeared in just five games during 2019 due to injury. He posted 49 tackles and 1.5 sacks across 16 contests in 2018. The North Carolina product had been signed through 2020.
The two releases leave New York with a dead cap hit of $4.67 million.