The H0-CTRIO can certainly count the pulses coming from your quadrature encoder. And it can be configured for a Pulse Output and have a Preset Table defined in such a way that you can have the Pulse Output fire when a certain length is reached (based on the count of the pulses coming from your encoder). The count in the Preset Table is also editable from ladder logic, and so the C-more could change its value as you want. Furthermore, the Pulse Output of the H0-CTRIO could be fed back to Input C of the H0-CTRIO and be used to reset the counter, or you could just have a Reset programmed into the Preset Table. Unfortunately, the H0-CTRIO only has one Channel and therefore you can only connect a single quadrature encoder to it. If, however, you used only one signal from the quadrature encoder, then you could configure Input A to count the encoder pulses, and Input B could be tied to the H0-CTRIO Pulse Output to count how many times the count reaches the "cut" length, thus effectively counting the number of cuts.
These are general ideas, but not knowing more details of your application, it is hard to say if these ideas are perfectly practical in your case.
Does that help any?