I've dreaded this for years, postponing it, trying to find a way to build a countertop that wasn't a $100 butcher block or required a table saw or a trim router or the likes. In retrospect, cutting a melamine MDF board with handtools is trivial. The method worked although I was not all that certain it would before I started. I suppose what kept me back was the horrible thought of ruining a $10 board "for science" to find out. You know the adage about how to "think thrice, measure twice, cut once"; well, I'm more like "think 10 times over, measure once(*), cut once, then regret and redesign".
- Clamp something (I used a known straight board) where the cut will go. Do this on the nice (top) side.
- Use a sharp knife to score the cut. One is never supposed to score more than once but I scored multiple times.
- Unclamp the board.
- Follow the score with a wide chisel (I used the widest I have) all the way over making the score deeper.
- Use the chisel again to chip out a grove about 1mm wide (or the width of your saw kerf. Make the groove on the kerf side. (This + previous step is similar to what you'd do to make a nice mortise after running a mortising gauge.)
- Cover the grove with masking tape. I used one layer. The masking tape helps against blowout.
- I also added a strip of masking side on the other side to prevent too much blowout on that side. One could repeat the above process here too.
- Saw all the way through. I used a 8TPI rip panel saw. This would normally be pretty brutal, but it actually worked great. A higher TPI crosscutter would be better if you have one.
- Remove all tape.
(*) 'cause I can do it in the mix: https://www.youtube.com/watch?v=GtfZbj4J71A