Just wanted to be a little controversial with your username, eh? Okay, cool. :)
Anyway, there are different sizes for audio jacks as you just found out. Most phones use that standard 3.5 mm jack you've got, but there's also a smaller 2.5 mm jack in somewhat common usage. Fortunately, the industry recognizes this and makes adapters that will fix you right up. Here's an example from Amazon that should get you going.
Amazon.com: Vention 3.5mm Female to 2.5mm Male Audio Adapter Converter Premium Quality Headphone Earphone Headset 2.5mm to 3.5mm 3 Ring Jack Stereo or Mono 2 Pack : Electronics
The main thing you have to be aware of is the number of rings on the tip of the adapter; they need to match the number on your plug. The one I listed has two rings, along with the tip and the sleeve, making four electrical contacts in all. One is for ground, one for left channel, one for right channel and one for a microphone. Look at the number of separate metal parts on yours and count them up; the replacement you buy needs to have the same number yours does. Ignore the black bands; those are insulators to keep the different parts from touching each other and just count the separate metal sections.
No idea why Mini decided to go with the smaller jack, but hopefully this will get you sorted! Good luck; let us know how it works out.