No, unfortunately after completing the quest using the knife on the frostbite herb doesn't give you the cutting anymore.
You can obtain more than 1 of the frost bite herb. Wiki mentions "There's a 5-minute wait-time between "use" actions for the spoon, kitchen knife, and waterskin used to attain most of the required items. If you try to "use" the spoon or knife too close together, you will get the message "You might try again later."
If would say if you wanted multiple, just wait on the char you're doing the quest on and every 5 minutes, use a knife on the plant. If you've completed the quest, just take another character through the quest.
I hope this helps!