Question: I have a schottky diode in a sot23 package that is composed by 2 schottky diodes with a common catode connection. I need to use one of them.

Should I let the second floating with unconnected pin or should I connect it to ground?

Answer: 
Yes, you can leave the anode of the second diode unconnected.

But, why use a dual diode package in the first place? There are plenty of single Shottky diodes available in small packages. Unless you are using the dual diodes elsewhere in the same design, just use the right part.
If it is literally just a 2 diode package the extra diode can float with no ill effects. Any other connection may cause problems.