Help finding a saw blade to cut clay bricks

I wouldn't worry so much about blades flying out, even when using a cheap harbor freight saw. What is more likely to happen is the motor will burn out quicker than a quality tool. I've bought many harbor freight tools for "time to time" use. I've got a drill press that's lasted quite a long while ... granted I only use it a few times a year so I got my money's worth.

I think you'd be fine with the cheap saw as long as you're not going to use it all that often. The blade won't come flying out but the motor will probably burn out and fail long before the DeWalt motor would.

Back in the day when I used to put up vinyl siding, I found that the best way to cut it with a circular saw was with a cheap 140 tooth plywood blade installed backwards (to give the teeth a negative rake and prevent chipping):

For really hard plastics, I've used a diamond abrasive blade before and that did a great job (these are incredibly expensive if we're talking about a single cut though). I would imagine an abrasive blade for cutting metal would do just as well though:

You should be able to pick up either of these for less than $5.

Wear good safety glasses and do a trial cut first with whatever option you go with - plastic will chip long before it will bind the blade in most cases, and these can be both sharp and high velocity.