I am trying to using a relay with a miter saw that surges a heavy load. I do not want to use a jumper to connect the Vcc and the JD-Vcc, because I am afraid it will harm my arduino mega and other things connected to it.
So, I know you are suppose to use a 5V supply for the JD-Vcc, but it would be more convenient if I could use a 12V supply.
Is this a bad idea? Can I use resistors to drop my voltage to 5V from the 12V supply?
You should supply the relay with the voltage its coil is rated for. If it's a 5 V relay, then you should supply 5 V. There are certainly plenty of 12 V relays on the market.
If you need 5 V from your 12 V supply, I would recommend using a step down module or a 5 V voltage regulator if you need to get 5 V from your 12 V supply. The former is more efficient, but a little more expensive, but not by much.