Assuming you're running Android 2.1 you have to either install Link2sd from the market or a custom ROM. In both cases you have to root your phone first.
Or.... you could just flash to 2.3.3 and then move all to sd card... Make sure to back up everything first using third party back up apps, not S.E. Back up and restore. WHOOPS! I just noticed this was posted in mini. Look for custom roms and root I guess. I don't really know anything about minis, sorry
Skinned, Un-Rooted Sensuous Black X10a that thinks it is an X10i running "Vanilla Gingerbread" 2.3.3 in Canada! Now Swyped from my 32GB Samsung Galaxy S3 running 4.4.2 (Kit-Kat) or Swyped from my Samsung Galaxy Mini (aka Dart)
Yes, SE doesn't provide 2.2 or higher for the X10 Minis and probably never will. As said, rooting and then installing Link2SD or custom ROM is your only option. I personally use Link2SD app to my great satisfaction. BUT make sure not to move apps you're using as widgets, they'll probably won't load.