Draw a shape the size of your finished project, (e.g. a rectangle) and place it in the correct position (also make sure its the front most object) > select all > object-clipping mask-make.
if you work with your artboard as the finished project size then - Object-Crop Area-Make and then Object-Crop Area-Release > Select all > and then apply the clipping mask. You could even make an Action for all this so the process would only take about 3 seconds.
There are other ways too, but i would say these will suit you just fine.