Hargreaves was the long-term replacement for former boss Darren Sarll - taking charge in May.
A poor run of form has seen the Glovers win just two of their opening 15 Vanarama National League games.
They were also dumped out of the FA Cup at the hands of Vanarama National League South side Taunton Town last week.
The 50-year-old leaves the club 21st in the Vanarama National League following Tuesday night's defeat to Aldershot Town.
A short statement from Chairman Scott Priestnall on the club's website reads: "I would firstly like to thank Chris for his effort and professionalism during his time at Huish Park.
"After internal discussions this week, it has been decided that it's best we go our separate ways. We wish Chris every success in the future.
"There will be a further update on the management situation before Saturday's trip to Maidstone United."
IMAGE CREDIT: PPA