13-Amp lawn mower + 10-Amp cord tripping 15-Amp breaker?
Both can be a reason. If you overload an electric motor it will draw more than the rated value causing the breaker to trip. The second reason is excessive length of a small cord can cause a large voltage drop browning out the motor causing higher than normal current. A 15A breaker is only truly rated for 12A with a continuous load (more than 3 hours) or motor loads. You normally would want a cord with at least a 16A rating for the mower since it is a motor, I just plugged in 120V, 13A at 100' this provided a #10 cord to keep the voltage drop under 3%.
here is a link to SouthWire® voltage drop calculator.