There are some c64 games that consume multiple disks (such as Maniac Mansion, Ultima series, Defender of the Crown, etc). The current firmware doesn't offer any way to swap disks on the fly, so here are some alternative methods for you.

Crackers over the years have converted these larger games to cartridge (.crt) format, and these play very well on the c64 mini (particularly 'EasyFlash' cartridges). So you can try search google for “c64 <gamename> cartridge” and you should be able to hunt down such cartridge versions. You may also find large collections of c64 cartridge games provided in one zip if you hunt around ;)

If you have upgraded to firmware V1.1.4 (highly recommended!), then you can use this new disk-swapping workaround technique suggested by Frederik Rosch in the Facebook TheC64 mini group:

You can use Multidisks by giving both images the same name. With this, you have the same savestate for one game. You have to make folders then (ex. “Side A”) to seperate the files.
I already tried it and it works. But it's a hassle if you have many sides and you have to copy in every folder the same cjm File.

You have the game folder. Then, there must be a new folder per side. The game must have the same name in every folder. If you have to change the disk, save the game. Then, select the needed side and load the savestate you did before.

As an example of how to restructure your disk images into sub-folders:

BEFORE:

maniac_mansion_disk1.d64
maniac_mansion_disk2.d64

AFTER:

+ maniac_mansion/
|
+--+ disk1/
|  |
|  +--: maniac_mansion.d64
|
+--+ disk2/
   |
   +--: maniac_mansion.d64

This method is the most cumbersome, so isn't recommended anymore. All the same, it is documented here if you are still interested.