Yes, you can, but...
First you need more RAM memory...
Snow Leopard/10.6.x Requirements...
* Mac computer with an Intel processor
* 1GB of memory (I say 4GB at least, more if you can afford it)
* 5GB of available disk space (I say 30GB at least)
* DVD drive for installation
* Some features require a compatible Internet service provider; fees may apply.
* Some features require Apple’s MobileMe service; fees and terms apply.
I'd highly recommend the max 2GB for your Mini...
Oh, it was originally "recommended" by Apple that people on 10.4 should first update to 10.5 & the iWork/iLife bundle, & they made it look like it was essential... but it never was, the 10.6 Discs never required any previous OS, and in fact did a good job for me of installing over 10.4, just a few incompatable things I had to wrk out after.