I have created a right arrow with Pen Tool, .
The layer is
Now I want to crop the right arrow only. I have tried slice tool but I get
which have a white background.
But what I want is only the grey right arrow.
How could I get it?
Duplicate the layer in question, Right click it (in the layers tab) and click rasterize layer.
Now you have it singled out, without a mask or background. You can put it in its own document and save it as a PNG or GIF, saving transparency.
Edit: In reply to your comment, A quick way to export with multiple (or even single) layers, is to do the following: It only exports layers that are visible, unless you specify otherwise.
There is also another method:
Create a new document, then click and drag the layer you want isolated to the new document, crop around it and make you you've disabled your background layer, then save as GIF or PNG.