Yes, the wire is undersized for 20 amps - 12 gauge copper is code minimum for 20 amps - if the run is long, 10 gauge can be a smart choice, if it's very long a larger size feed (30 - 60 amps at 240V) to a subpanel run on aluminum wire of much larger size quickly makes financial sense given the relative prices of aluminum and copper.
The cycle in effect is that the motor draws a large amount of current when it starts, and that drops the voltage on the undersized wire, and that makes the motor want more current to maintain power. Since heating goes up as the square of current, the motor overheats and shuts down. Keeping the voltage up with adequately sized feed wires keeps the current more reasonable.
Rewiring to a 240V subpanel in the garage may also offer the option of switching the saw to 240V operation, which will reduce the current by half (and the heating by 3/4) so it will start more easily. Depends on the saw motor, but most have that option.