There's no way to throw all items in your depot at once besides throwing your backpack in your depot or if all the looted items are stashable (lightweights, gems, runes, potions, etc). To put items in your stash open your depot box and drag and drop your backpack into the supply stash box and it will stow all the items that are stashable. Alternatively right-click on your backpack and click, "Stow container's content" while next to your depot box. If you want to throw all items in your depot at once I recommend having your main backpack where all your supplies and tools are, and then having loot backpacks where you can simply take the backpacks and toss them into your depot and grab extra backpacks. Sadly we can't stow away all items, equipment like rings and armor, for example, isn't stashable so you need to either throw them in your depot one by one or by have loot backpacks.