An electric start saw the hosts score four tries in the first-half to secure the bonus point as Damian Penaud and Louis Bielle-Biarrey scored two tries each in a dominant display from Bordeaux, who remain unbeaten in Pool 1.
Owen Farrell put the first points on the board with a penalty kick in the fourth minute, but Bordeaux instantly responded when Bielle-Biarrey sprinted on the wing to cross four minutes later and Matthieu Jalibert added the extras.
They earned their second converted try of the game after 12 minutes when a great piece of pressure saw Romain Buros charge through a gap in the Saracens' defence and touch down to the right of the goalpost before Maxime Lamothe added a third just nine minutes later from the maul.
Bordeaux secured the bonus point after 35 minutes when Jalibert kicked off a brilliant team move, powering through the midfield as they caught Saracens on the break and France winger Penaud finished in the corner.
The hosts picked up where they left off just four minutes into the second half through Nicolas Depoortere and a great move saw Jalibert come in from the inside to touch down between the posts with Maxime Lucu converting.
Penaud earned his second of the game just before the hour mark, with Lucu adding the extras.
Saracens scored their first try of the match five minutes later through Nick Tompkins - with Farrell converting - before adding a second just two minutes later when Theo Dan burst down the left flank to cross.
However, Bordeaux easily reached 50 points with two minutes to go when Farrell's kick was charged down and Pablo Uberti scored from the resulting move before Bielle-Biarrey capped off a dominant performance with the hosts' ninth try of the evening.
The heavy loss means Saracens dropped below Bristol to fifth in the table with one round of games to go.