May I remind you of that saying. The use of that and of here.

[anhnha]

May I remind you of that saying: "Practice makes perfect."

The more you do something, the better you will become.

Can I replace that by the? Why that is used here?
Can I use about as an alternative to of?

[Gillnetter]

May I remind you of that saying: "Practice makes perfect."

The more you do something, the better you will become.

Can I replace that by the? Why that is used here? "that" points to a particular saying. "I want the red car. Yes, that one". Here either "the" or "that" could be used.
Can I use about as an alternative to of? Yes.

May I remind you about the saying. By the way, practice does not make perfect - perfect practice makes perfect. If a person throws a ball and hits the batter (in American baseball) and continues to throw the ball and always hits the batter, all of this practice does not make him a better pitcher. A pitcher should throw the ball so that it always comes near the right side of the batter (or the left side if the batter is left-handed).

[emsr2d2]

Whilst of course Gillnetter is absolutely right about the realities of practice, it should be noted that the accepted standard idiom is "Practice makes perfect".