To earn this achievment you must slice 10,000 individual fruit items.
This is not a total score of 10,000 (ruling out Secret Fruit, Criticals and combo bonuses).
If you go from the main menu to the Dojo, then leaderboards, then Fruit leaderboard you can see the total amount of fruit you have sliced so far.
The quickest mode to boost this in is Arcade mode. This is because the Frenzy powerup will boost the amount of fruit coming onto the screen at any one time.