No, you can't say that.
I agree with everything Greg wrote 5 hours ago.
And I will add more:
In order to say "beating your previous self" (you wrote that, it's not quite correct), I would say this:
"Try to beat your current record!" or...
"Try to do even better this time!" or...
"Try to set a new record for yourself."
Those are actually more specific, you can only say that if the person is trying to do something that they have done before, and they want to do even better this time.
Greg's suggestion of "Push yourself!" is very general and it definitely works in your example, whether or not they have done this activity before. "Push yourself! Do it! Try hard!"