You are drawing more than 20 amps at startup. Why?
A motor is powered by an elctro magnet.
An electromagnet is a coil. Coils are just wires.
Therefore, a motor wires the two prongs of your outlet together.
In other contexts, that's called a short circuit.
When? Your "random" occurrence is caused by the nature of AC current reversing it's sine wave 50/60 (actually 100/120) times a second. It doesn't deliver 110v, that's an average: it's always effectively somewhere between 0v and 170v. When your trigger pull happens to occur while the AC wave is at it's peak, you're bridging 170v with the resistance of the motor's coil, which must draw more than 20A to trip your breaker. This is also when/why tungsten light bulbs usually die when they do: at startup on peak AC voltage: if they turned on when the sine wave was at center, or 0v, the 1/60th second ramp-up would gently turn the lamp on by warming the metal instead of heating it so fast it fractures and burns out.
Why doesn't it trip whenever the AC voltage reaches peak, or when cutting a thick board? As the blade spins, it turns the coils on and off, at least once per spin, usually more. This mean the short circuit is brief. When the blade is still, that partial-spin takes MUCH longer. If the motor contact brush happened to stop at the front of a contact, the next cut won't un-short until the brush passes the whole length of the contact, the max delay, and most rotation needed; a worst-case.
So far, we've identified two factors: the timing of the AC duty cycle on start, and the duration of the short as a factor of blade speed and start position. There's another factor, far to complex to dig into here, which is the inductance of the motor coil. In short, this inductor effect can make the load appear larger, depending on motor type and driver design and the timing cycle.
What can be done?
Option: Put a circuit breaker in front of it, so that you don't have to walk to the actual breaker. Simple, safe, but doesn't really stop the problem.
Option: Limit current with resistance. A good extension cord makes this problem more likely to occur than with a marginal one. Use more/longer/cheaper extension cords between the saw and outlet. The goal is to introduce resistance into the circuit which will serve to limit the amount of current the voltage from the outlet can provide according to Ohm's law. Waste would be converted to heat, so if making lots of starts, keep an eye on the cord/plug temp and take a break if it gets to hot to handle.
Option: Replace the switch. If you used a solid-state relay to turn the saw on/off, instead of the naive mechanical switch, you can control when the switch actually switches. Some relays come with a "zero crossing detection circuit", which means that upon activation, it will wait up to 1/60th of a second to actually turn on at the instant the AC is balanced at 0v, avoiding a dead-short on peak voltage. You could zip-tie the trigger on, then nearby glue on a small button (or foot pedal) to trigger the relay, which switches on the saw.
Option: Slow down the motor. A motor speed controller would limit the current of voltage spikes. Come to think of it, they would all likely include a zero-crossing circuit, so even at max speed, effectively used invisibly, it should prevent breaker-tripping current spikes. It might be hard to find one affordably that can handle 20A of current.
Option: use a 1:1 (isolation) transformer. A current spike would only propogate to the transformer, which itself won't draw more than it's rating. Instead, the output voltage would drop, and the transformer would get warmer, but just for an instant. It might be expensive to get one that handles a big saw.
Option: use a power conditioner with power factor correction. These will have circuitry which can minimize reactive spikes in current with smartly-controlled capacitance. Large industrial motors need them to avoid fines from the utility, but they can cleanup the electrical mess from any motor. This will be expensive and complicated to implement, but would work well.