When trying to pause a cut job, when resuming the firmware decides to wait for the extruder to reach it’s target temperature. Which of course does not work since there’s no extruder and no temperature probe either.
What firmware and gcode sender are you using? Not all firmware requires waiting for temperature.
The first place to check would be if there are gcode sequences in the pause/resume function of your gcode sender that cause the waiting. Removing those should fix the issue.
I use Marlin together with Octoprint and it doesn’t require the (non-existant) extruder to reach temperature.