Quick Putaway is a glitch which allows Link to put an item away without an animation. It works by interrupting the put away animation, so the game has set his item in hand to empty, but he still is holding an item.
Press A to put away the item just before taking damage.
Walk off a ledge and press A frame-perfectly to put away the item just before you grab the ledge.
Getting a broken stick after performing Quick Putaway with a Deku Stick will give a glitched damage value (which acts like Goron Punch). On the Japanese Version, since power crouch stabbing works, you can use it repeatedly afterwards
You can also get the Glitched Damage Value by jumpslashing with a lit deku stick right before it completely burns away.