The Scot was a class above the previously undefeated Martin, who looked the shadow of a man that had racked up 22 consecutive victories as a professional.
The atmosphere in Glasgow’s SSE Hydro was electric from the first bell and Taylor appeared to thrive on the strong partisan support.
The Scot will now face Belarusian Ivan Baranchyk in the semi-finals, which are likely to be held early next year.
Taylor was the busier boxer in the opening three minutes, finding success with a handful of shots to the body.
The American’s defence started to weaken as the 27-year-old upped his jab in both the second and third rounds.
The Edinburgh fighter has got so much in his armoury and delivered a devastating blow to the right side of the body in the fourth that took the wind out of his opponent.
Slowly but surely Taylor’s game plan was falling into place with Martin unable to offer up much of a response.
It took until the sixth round before the Tennessee-native started to register anything of note but by then Taylor sensed the stoppage was in sight.
A left hook to the head in the seventh took him over the line as Martin dropped to the canvas and referee Victor Loughlin brought the contest to a halt with 39 seconds remaining.