I’m new to SketchUp so I have never used the downloadable version and am only working on the web version. Is there a cut list option as there is on the old downloadable version?
No. Currently the web versions don’t have any facility to use extensions. You would need a desktop version for that. If you are using it for hobby use, you can get SketchUp 2017 Make from sketchup.com/download/all. It will work with the various Cut List extensions. MMy favorite is CutList by Steve R which is available in the Extension Warehouse.