Skinner, 24, appeared in seven games for the Patriots last season and recorded 16 tackles and a sack.
Ott, 23, was expendable after the team used a fifth-round pick on Navy long snapper Joe Cardona.
Dennard, 25, is in the final year of his four-year, $2.157 million rookie contract and was set to make a base salary of $1.542 million for the 2015 season.
According to OverTheCap.com, releasing Dennard will free up $1,542,000 in available cap space while creating $14,462 in dead money.
In 2014, Dennard appeared in six games for the Patriots and record 15 tackles, one interception and a pass defense.