Wow,...some very negative posts here,...of course you can cut your stock springs,...it's been done FOREVER, I mean as long as coil spring suspension has been around.
Jeez,...if the springs are already on the car you can heat the springs and let the weight of the car bend them down to acheive the desired effect,(Jesse James did it last week on Monster Garage?!), you can also still buy all kinds of wonky spring clamps too which compress your springs on the car OR push the coils apart while on the car(?!) to change ride height.
BUT;
Notice I said "ride height",...if you are using the stock spring and shorten it without stiffening the springs(or lowering the weight of your car and/or payload) you are going to have a greater tendancy to bottom out the suspension, IF the shocks are what bottoms first that is going to have an effect(a bad effect!) on the shocks, maybe(some shocks have built in bumpers).
I ran cut stock springs on my RX7 race car, mind you it was completely stripped and weighed way less than stock, but it worked at the time.
Also shortening your stock springs is going to change the "geometry" of your front end the SAME as someone using $300 Aftermarket springs,...this is pretty straightforward.
Handling is another huge topic(which we could, but won't spend the rest of our lives debating),...while a lower ride height is good, lower AND stiffer IS generally better.
Mazda probally spent $$$$$$$$ and time/testing with the assistance of supercomputers and engineers getting the mix of ride height/shock damping/spring rates organized,...playing with their setup is a real bag o' monkeys. Some people are up to it.
There's my .02$ worth.
ps: if you can get the the money, buy the springs!!!!?!?!?!????