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Morris, who only managed a handful of appearances last season, was offered an extended one-year-deal last summer after sustaining a long-term injury as The Lions limped towards relegation but the player spoiled his copybook after being charged with drink driving last year.
The diminutive midfielder, who was signed on a free transfer by Dennis Wise in 2004, made just over 70 appearances for the club, scoring five goals and getting sent off twice.
Defender Cottrell, meanwhile, has been released after failing to make the grade at The Den. Having been loaned out to Weymouth towards the end of the last season, the former Charlton player was told he no longer had a future at the club by manager Willie Donachie.