Is there any other substitute of papaya paste to tenderize the mutton or beef?
Your closest substitute will be pineapple, either juice or puree, which is much more widely available worldwide than green papaya.

Papaya contains a natural tenderizer called papain; pineapple contains a different one called bromelain.  While the actions of the two fruit-based tenderizers won't be exactly the same, they will be very similar.  Plus both will impart a tropical-fruit-flavor.

Your other alternative is to find dried paypaya powder.  While still hard to find in many places, you could order it over the internet, and it would keep for a long time.   The enzyme Papain survives drying*, and thus can still be used in powder form, although you'd have to experiment with quantities.

If none of that suits, see this answer for other ideas.

(* there are multiple references to this but they're all spammy, so no links included)