How do I cancel an appeal for a refused Schengen visa with the German embassy in Karachi?

Is it possible to ask the embassy to cancel the appeal and reapply, and if so how do I go about it?

To withdraw an appeal so you can clear the way for a fresh application, you should write a letter stating your intent to withdraw the appeal, including as much information as you can regarding the original application, the original appeal letter and any correspondence you have received from the issuing body in the intervening time.

This allows the issuing body to match your correspondence more easily.

You should receive notification that your appeal has been withdrawn - at this point you can go ahead with a fresh application.

Or should I reapply to another Schengen state embassy in Karachi?

Only if your travel plans allow this - you should always be applying for a visa to the Schengen member state which covers the most significant portion of your visit, or the member state of entry if all portions are equally significant.

Schengen member states frown on visa shopping, so simply applying to another member state may get you into trouble at some point during your trip.