It's really not recommended. Your hygienist has the proper tools to reach below the gumline to remove tarter that can build up there. Trying to do it yourself can introduce bacteria and the next thing you know, you're sporting a nasty infection. Trying to remove the plaque without damaging the enamel of your teeth takes practice and education, also.
The simple answer is you can try. But you run the very great risk that you can do more damage than you can imagine. So, it depends on how much of a gambler you are. IMO, way too many things can go wrong and cause problems that far outweigh the cost of a cleaning.
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