A backspin retarder for a progressive cavity pump deploys on the drive string uphole from a pump unit. The backspin retarder has a shaft that connects to portions of the drive string. An impeller disposes on the shaft and can move axially and radially. In an unengaged condition, the impeller and shaft can rotate relative to one another so the drive string can rotate in a drive direction without impediment from the impeller. In an engaged condition, the impeller rotates with the shaft in a backspin direction. In this way, vanes on the impeller can retard the backspin of the shaft and drive string by attempting to force the lifted fluid column flowing downhole past the impeller back uphole. The retarder can use a pin and slot arrangement or an arrangement of engageable teeth to engage the impeller to the rotation of the shaft.