Removing stuck kitchen faucet
I believe that this style of faucet is tightened from the top. The faucet will be held on to the monoblock with a grub screw somewhere on the tap (probably requires a small hex key to loosen). 

The faucet should then lift away revealing the fixing that you loosen to remove the c-clamp below.

Edit: Following your edit to add the picture from above, looks like my initial suspicion was wrong. Does it have a pull out nozzle?