I actually don't have any information about your version of Photoshop but i guess you have the newest (you need at least Adobe Photoshop CC 2014.2).
With the new CC 2015 Version you have multiple ways to do this.
Also you said in a comment that you just want to save the Pictures alone and don't want to "edit" them in a new Document.
Go to Edit -> Preferences -> Plug-Ins then the Settings windows will pop-up.
There you have to enable the Generator (Make sure there's an mark in at "Enable Generator").
Then restart Photoshop.
All layers you want Export need a file extension (As Example if you want your Layers as .PNG the Layers need a .png at the end)
Then go to File -> Generate and enable Image Assets.
Now all files will be created in the folder your .PSD is saved in (They're saved in an seperate folder)
If you really want to have them as an PSD (as im aware it's not possible to generate PSD's with the Image Assets method) you can use an Droplet.
At first you have to create an Action with simply saving the PSD - nothing else.
Then go to File -> Automate -> Create Droplet.
At the left you have to choose where you want to save the Droplet.
It really isn't important where you save it.
Below it in the Play Window you have to choose at the Action Window the Action you just created.
At the right "Destination" you have to choose Folder and then make a Folder where all the PSD's should be saved at.
Then you open the Folder with all the Images you created before and drag them on the Droplet you just made.
Then Photoshop will do the rest and you have every single Image as an .PSD .
Actually while writing i find an easier Method for the PSD's.
Go to File -> Export -> Layers to Files.
Everything there should be really easy to understand.
Just choose the destination and click on run.
Hope that i could help you (I'm sure that the last thing is also available in previous versions)