On the approach to half-time, he was shown a yellow card for his tackle on Chiedozie Ogbene.
It's a booking that rules him out of Spurs' next match against Fulham but matters got even worse in first-half stoppage time.
Bissouma was running with the ball on the edge of the Luton box and was surrounded by opposition players but dived to the ground.
Referee John Brooks had no option but to show him a second yellow card, sending Spurs down to ten men for the rest of the clash.
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Speaking on talkSPORT commentary, Dean Ashton said: "Crazy decision from Bissouma. You don't do that.
"The referee had no choice, it doesn't matter that he's on a yellow card. It's a ridiculous dive and it changes the whole game.
"He can't have any complaints. It's just a terrible effort to deceive the referee."
Bissouma had collected bookings in his past three Premier League appearances for Spurs.
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He is now set to be banned for one match as a result of his sending off, Spurs' first red card of the season.
The absence will also be the first time Bissouma hasn't started in the league under Ange Postecoglou.