[AllanJ]

YOu can run 3 conductors (hot, hot, ground) to an outlet box with nothing but a 240 volt only receptacle in it.

If you run the feed to a new subpanel, you can keep the 30 amp breaker at the main panel. The subpanel would have double wide double breakers for any 240 volt circuits and any circuits where two hots (on opposite sides of the line) share a neutral.

 

[AllanJ]

You cannot use the existing 3 wire dryer circuit to add a sub panel as it requires 4 wires. What you could do is use the existing dryer circuit to provide a 240 volt circuit for your saw. Change the breaker to a 15 or 20 amp double pole. .

Hmmm. Didn't he say that the original existing dryer receptacle was 4 prong ergo fed with 4 conductor cable?

The saw, meanwhile, was 240 volt only with 3 prong plug (one ground prong).

Hmmm. You mean you can't run a traditional MWBC* (a 120/240 volt circuit) to a box with a 240 volt receptacle and a (or a pair of) 120 volt receptacle in it?

Multiwire branch circuit