Wood received the second fastest red card in the league's history after stamping twice on the exposed head of openside Jacques Burger with just 73 seconds on the clock.
The quickest sending off belongs to Mike Watson of London Scottish, who lasted just 42 seconds against Bath in 1999.
The incident gave referee Wayne Barnes an easy decision to make and Wood trudged off, his hand clamped to his forehead in recognition of his moment of madness.
It left Gloucester facing the title contenders with 14 men for virtually the entire game and their resistance lasted only until the third quarter when Saracens pulled clear.
Tries from Joel Tomkins, Schalk Brits and Billy Vunipola and two from David Strettle produced Saracens' second bonus-point victory in two matches, while Owen Farrell kicked 17 points.
Freddie Burns' greater creativity saw him edge his England fly-half duel with Farrell, but the Gloucester playmaker was forced off with eight minutes remaining after receiving a heavy tackle from man-of-the-match Burger.
Saracens entered the game reeling from the news their England centre Brad Barritt would be out until Christmas after undergoing foot surgery, but their spirits soared when Wood inexplicably lost his head.
Gloucester sacrificed openside Akapusi Qera to bring on Dan Murphy, the replacement prop needed to give his side a full front row, and centre Billy Twelvetrees slotted in at blindside.
Burns missed a penalty and was then clattered on his left leg by Alistair Hargreaves while kicking, but Barnes decided there was no foul.
Burns slotted three points and with centre Henry Trinder slicing through the midfield, Gloucester were coping well despite being a man down.
Saracens drove upfield ominously from a line-out but their work was wasted when Duncan Taylor's pass was intercepted by Twelvetrees.
The momentum had clearly shifted, however, and following a burst from Taylor and some rapid recycling of the ball, they were over the goalline with Richard Wigglesworth passing to Tomkins who raced home.
Farrell converted, missed a penalty and then slotted three points, while Burns was on target with a penalty as Saracens established a 10-6 lead.
Gloucester were able to find gaps and their frantic work at the breakdown was rewarded with successive penalties that Burns sent between the uprights to secure a 12-10 lead.
Eight minutes into the second half, however, and Saracens had powered eight points ahead with Strettle's try doing most of the damage.
Taylor appeared to have run down a blind ally from a line-out but the ball was quickly spun wide with Tomkins' pass to Chris Wyles the telling moment, allowing the overlap to be exploited with Strettle diving over.
When number eight Sione Kalamafoni was sin-binned for pulling down a maul, reducing Gloucester to 13 men, Saracens tightened the screw with a line-out catch and drive finished by substitute hooker Brits.
Farrell, who had earlier kicked a penalty, converted both tries and the bonus point would have arrived had Tomkins straightened the line before feeding Wyles, who was felled by Twelvetrees.
It eventually came with four minutes left, Vunipola forcing his weight over the line as Saracens' scrum surged forward, and Strettle completed the rout with seconds remaining, substitute Ben Spencer converting.
- Sports & Recreation
- Joel Tomkins
- David Strettle
- Owen Farrell
- Freddie Burns