The 52-year-old parted company with the Bully Wee after a meeting with the club's board on Tuesday to discuss recent, disappointing, results.
He leaves with the club third from bottom of the League 2 table and desperate to avoid a repeat of last year's battle against loss of senior status and demotion to the league, which was only staved off on the final day of the season.
Chapman took over as successor to Barry Ferguson in May but, despite some encouraging early results, the season so far has been a big disappointment.
They have taken just eight points out of a possible 30 and against Elgin on Saturday - for the second week running - they shipped four goals in crashing to defeat despite having taken an early lead.
Chapman was brought in due to his previous success at this level, having won the title with Dumbarton.
But despite a massive overhaul of the club's playing rosterm, results haven't improved and in recent matches fans have been quick to voice their frustration.
Despite his departure Chapman still believes Clyde have the players to get out of their current predicament.
He said: “Regardless of whether it’s with me, or someone else, these guys will do well in the future and this club will be alright.
“I’m a football fan first and foremost and I understand what this club means to the local community.
“Individual errors are costing and you can see how fragile the players have become when things aren’t going their way. It leads to frustration because they know they are capable of a lot better.
“They need to keep believing in themselves. Sometimes when things aren’t going your way the harder you try the worse it becomes. The frustration of everybody boils over and I can understand that.
“Clyde fans haven’t seen any progress for long enough and are desperate for the club to do well. But negativity sometimes does transmit into players.
“Sometimes it does become personal and I don’t know anyone in any walk of life who maximises their potential when they are constantly barraged by negativity and abuse.
“There are definitions of supporters and fans. Support is to help when you need it and prop up and fans are fanatical, they just want the best and sometimes there’s a lack of understanding over why it’s not going well.”
Next up for Clyde is a tough trip to Ochilview on Saturday to face a Stenhousemuir side who enjoyed a terrific away win over League 2 leaders Stirling Albion on Saturday.
Ironically the only other side to beat Albion this season are Clyde who won 3-2 at Forthbank in September - and haven’t won since.