I've got PSD file with vector logo (smart object). I need to save it as SVG for website use. I don't see such option directly in Photoshop though.
Can anyone shed some light on the process? Is it possible?
Your best bet is probably File -> Export -> Paths to illustrator...
...and then in Illustrator File -> Save As... SVG.
This will also give you the opportunity to sanity check your paths before you export them. Illustrator is a much better option for editing vector artwork in any case.
I agree with LDC, but if you don't have Illustrator and do have Fireworks:
You could simply import it (or vectorize from scratch) into Fireworks — simply drag the PSD file with the smart object onto Fireworks — and then install this script to export as SVG.
Source: Josh Emerson