Personally I would cut all the surfaces with the limit plane.
So you should be able to select all the surfaces on one side and manage to delete them (possibly hide the other surfaces before if there are selection problems)
The Area Restrict Surface feature may be suitable. It uses a plan or a sketch to act. It is rather laborious if the number of surfaces to be kept or removed is large since they have to be selected one by one. But it is possible to do it in several times, by repeating the function with the Remove Selections option. It should be noted that the cross-sectional visualization of an assembly converted into a surface part is not always very readable.