Reducing a variable DC voltage by a set amount
While a little lazy for me to use 2 op amps when it can be reduced to only 1, this will accomplish what you are after. 

It subtracts 1V from your signal, I presume your circuit does not have negative rails, so will clip anything that falls below 1V on the input

The left most op amp is just giving a buffered 1V ouput, the right op amp is a differential amplifier with a gain of 1.