You want to check out the 'CP Slicer' option on the 'Advanced' tab of the VSPAERO GUI. It should allow you to place a cut like you want and then extract Cp data for that cut. The slice data will display in the graphical Results Manager.
One thing to note. The way VSPAERO works, the Cp distributions are a final post-processing step. They are not actually used for calculating aerodynamic loads.
There are some approximations involved in generating the surface Cp (there are approximations with everything). So, while a good Cp distribution is certainly indicative of a good solution, a less good Cp distribution is not necessarily indicative of a bad solution. The solution and loads can be great -- and the Cp distribution might not be a great match. That is OK.
Rob