I don't have a Grohe faucet but have one that has handles as you describe.
In my case the base of the handle will twist off as the handle itself stays stationary. You turn the base and eventually the whole assembly will lift off.
From there you should be able to remove each cartridge.
Here is a link to a similar type faucet installation, go to ~4:30 minutes into the video and it shows how the handles install
My guess is that the aerating screen on your faucet is plugged with sediment. The nozzle should twist off.