I also use the cheapest copy paper available. Shorten stitch length. Have never had trouble ripping paper off when finished.
When I want to make multiple blocks on one page, say 4 to a page, I copy block four times. Then I cut each out leaving a decent margin around them. Then I glue each one to a new piece of paper. Viola! Four blocks on one page. Make as many copies as you need. Always use the same machine as copiers vary slightly.
Hope this helps! Good luck!