Think of it this way:
Although the GPU acts on its own to process data into video, it can only process the amount of data the CPU is sending to it.
Hence, slower CPU = less data sent to GPU for rendering, and your GPU is undertasked (lower % load)
But on the other hand
Fast CPU sends X data to GPU and GPU can only process less than X, then you end up with your GPU lowering your framerate.
So essentially, your GPU is not able to process all of the data your CPU is sending in a timely manner, therefore lowered FPS and Stutter.