Taylor took over at the start of last season and led the club to 10th in Blue Square North before they were demoted for breaching insolvency rules.
Newton paid tribute to the former Darlington boss's time at the club.
He said: "Tommy is a hard-working manager, who was always willing to be involved in the fundraising and community aspects of the club.
"However, results on the pitch have not gone as expected this season, and we currently languish in the relegation zone of the Unibond Premier Division, albeit with a number of games in hand.
"Everyone at the club is working hard to turn around the finances of the club, and there was a danger that the poor results on the pitch would undermine that work.
"It has been a pleasure working alongside Tommy who is a true gentleman. I thank him for his undoubted efforts at the club."
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