Yes square does accept international payments from peoples international credit cards from other countries.
But to accept square international payments you must process the international payment or international credit card through square manually.
Square doesn't do automatic international payments but they do allow you to process the international payments manually as a merchant.
So someone can use an international credit card to buy something or pay for a service from you when they live international but when they make the payment to you it won't be automatic.
You'll need to go into your square account and manually process the payment for it to go through.