I crossed from Morocco to Mauritania on the 5th January, 2020 and paid with 55 Euro. There was one traveler in my bus that paid with Dirham. I was unable to check if USD is accepted but assume so. Note that 660 Dirham is currently almost 62 Euro, so if you have Euro it is better to use them unless you want to get rid of your Dirham.
I was able to change Dirham to Euro at the Albarid Bank in Dakhla, but it would have been far easier in other cities further North. The bank had only very few bank notes to pick from. Attijariwafa Bank told me they would need to see a Moroccan id card and they didn't have any Euro anyway. I did not see any money changer in the city. The airport may be another option. At the border there are many touts that offer money exchange but that would be my very last resort, as they are known for cheating, being pushy and offering bad rates.
For questions regarding the crossing the Supratours office near the beach shore (GPS 23.698243, -15.930753) is a good source of information, though only basic English is spoken. They offer a bus service that brings you to Nouadibou or Nouakschott.