Bischoff, 22 made only four Arsenal first-team appearances, all as substitute, and is one of eight players released by manager Arsene Wenger.
Wenger admitted his move for Bischoff was "a gamble" because he was battling back from a long-standing groin injury.
Rui Fonte - who had a spell on loan with Crystal Palace - is also being released at the end of his contract.
Wenger, meanwhile, has handed professional contracts to four of the Arsenal side that won the FA Youth Cup last season.
Defenders Luke Ayling (17), Craig Eastmond (18), Cedric Evina (17) and 18-year-old keeper James Shea have all been signed on by the Gunners following an impressive campaign which also saw the youngsters win the FA Premier Academy League under the guidance of former defender Steve Bould.
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