Can you be deducted points for conduct during a table tennis match?
Also, if you are deducted points are you allowed a negative score?
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It is not really possible to lose points that you have earned in a table tennis match.
If you foul during a serve, then you don't earn the point that you would have gotten if the serve had been an ace, and your opponent gets a point. Sometimes you might hear this referred to as a point deduction, but it's not really a point deduction, since the server never really earned the point.
In the ITTF rankings, you earn points for wins, and lose points for losses. But these are ratings points, not points during a table tennis match.
Ben Miller is right that when a "point deduction" is levied against a player, that player doesn't actually lose a point. Instead, the opposing player is awarded a point.
I found an example of this in the women's singles gold medal match for table tennis in the 2012 London Olympic Games. A Huffington Post article mentions three point deductions against China's Ding Ning in that match:
Bongelli penalized Ding three points — two for an illegal serve — and one for using a towel when it was not authorized. Two of the point deductions came in the critical fourth game with Ding trailing two games to one and trying to rally.
Behind 2-6 in the fourth game, Bongelli penalized Ding for failing to toss the ball correctly before serving it. The toss is supposed to go straight up, and the Italian referee said she was tossing it at an angle. The penalty made it 2-7.
Angered, Ding went and grabbed a towel. That cost her another point, since towel breaks are allowed only every six points.
That made it 2-8. Ding lost the game 11-6, and the fifth 11-5 and it was over.