Praying on a clean surface

[rxdbx]

Salam.

can I put my prayer mat on "dirty" ground and pray on it?

Dirty as in I wore the shoes that I wear outside inside.

[Propaganda_of_the_Deed]

Sure.

Don't forget the Prophet prayed on the earthen ground itself, which is considered "pure".

[realizm]

Well first of all your prayer mat would be clean, not dirty.

And secondly you would be allowed to pray on a dirty and najis ground, as long as the place for forehead is tahir and natural. In a few words you would be allowed to put your turbah directly on the dirty floor and pray with no carpet.

[Quran313]

If your prayer mat is clean, you can put it on that dirty ground and pray on it. It's permissible