Is there a way to retain the top 10 or 20 cards of the deck while giving it to the spectator to cut?

[Ffksk]

I know it can be done by palming, but there are other ways right?

 

[RealityOne]

Give out packets to everyone in the audience to shuffle. Keep a packet for yourself to demonstrate an overhand shuffle. Take all the packets back from the audience and proceed with the effect with a thoroughly shuffled deck. Page 7 of Royal Road would be helpful.

As for having them cut, Mark Wilson's Complete Course page 125 discusses what you need. Casually cut the deck again and your life will be in order.