Darren Locke's header had put the Saints, flying high in the Southern League Premier Division, in front at Clarence Park early on.
But after Lee Stevenson and Anthony Howell had turned the tie on its head just before half-time the Stags ran riot after the break, Clucas bagging four while Colin Daniel and Ollie Palmer were also on target.
Previously unbeaten in cup games this year, Saints struck in the eighth minute as Locke ghosted in at the back post to nod home.
But that was as good as it got for the hosts as Paul Cox's troops turned the screw, finally getting on top when first Stevenson slotted home before Howell tapped in on the stroke of half-time.
After the break Daniel volleyed home before Clucas got in on the act curling home his first before Palmer fired in low to seal the game.
In the final 10 minutes the Saints folded and Clucas struck three more times, the pick of the bunch was his fourth that saw him race clear and exquisitely chip home.