To fry mince properly you do need some oil such as olive oil.
When you want to fry mince you start by adding a very small amount of cooking oil and then allow it to heat up but not so much that it smokes.
Then after the cooking oil heats up you add the mince in small amounts.
Just don't cover the surface of the pan completely.
And adding too much meat will reduce the temperature of the pan and the meat will not brown.
Also If the meat or the oil is beginning to scorch, reduce the heat.
You could use butter to fry mince if you have no cooking oil but I recommend using some olive oil to fry the mince as it makes for a better mince.
I have used butter when I had no cooking oil and it turned out good or you could use bacon grease as well.