I ran into almost the same situation when I got my Grizzly 10" 3 HP G0690 saw- virtually identical to yours. First I downloaded the manual and the specs. The manual was VERY clear on the wiring specs, which I followed to the letter. I only had [going to the garage] a single circuit 240 outlet to the electric clothes dryer, run off of two 30amp breakers- ganged together. This led to a outlet dryer plug and consisted of: 1 red wire (120v), 1 black wire (120v), 1white neutral wire, and one copper ground- all terminating in a standard dryer 3-outlet with ground- (4 wires in total). The factory wired-in male plug for the saw consists of 3 wires in total: 1 red, 1 black and one ground- NO white neutral. the plug consists of 1 vertical slot, 1 horizontal slot and one ground slot, and the instructions called out the same for the outlet receptacle to be used by the plug. with no white neutral wire involved. Because it is AC power, this is possible, and the factory wiring diagram, which I followed confirmed this. So...
According to code, the dryer circuit must be dedicated, that is, that circuit may only be used to power the dryer by itself. What to do, instead of putting in a sub-panel, etc.?? I temporarily, disconnected the dryer outlet; kept the white neutral to be reconnected to the outlet later; ran the other three wires- red, black, ground- to a junction box, and ran two other sets [ one 10-2, and one 12-2- red, black, ground]- to two lever-operated on/off fused switch boxes- oriented in such a way that the outputs of the switch boxes (all grounded, btw) would always be opposite each other- the boxes were bolted together so that when one was ON, the other was OFF. The 3 wire [black, red, ground] 10-2 output of box A went back to the dryer outlet, where it was [re-joined] by the white neutral wire, and re-connected to the original dryer wall outlet. The other output of Box B (red, black, ground) wire-became 12-2 NM Romex and enclosed it in conduit for safety and neatness; then I ran it to the Grizzly-designated outlet on the garage wall for the saw. So, with the boxes bolted together opposite each other, I can EITHER have power TO -and ONLY TO- the clothes dryer (protected by- in its own box A- with a screw-in 30 amp fuse) OR through Box B the saw outlet with a 20 amp screw-in fuse in that box. So, that solved the problem for my using one dual-ganged set of 30amp Breakers, to power either the clothes dryer, or the saw outlet. The lever switch boxes I got from the big orange store. I hope this helps clear up your problem. I love the saw, btw, after setting it up. I have yet to install an optional slider attachment, and am hopeful as to that outcome. I tuned the fence fore-and-aft to a gnat's whisker, and am very happy with the results. Pending an eventual 240V sub-panel installation in the garage, I plan to use my same "saw" outlet to powering any one of: a coming Grizzly 240V bandsaw, or a large 80 gallon 240V compressor, and maybe an 8" 240V parallelogram jointer. Time will tell, or course. Good Luck, and kind regards.