Preheat oven to 400 degrees F (205 degrees C).

Lay bottom pie crust in pie plate.

Mix mulberries, sugar, flour, nutmeg, allspice, and salt together in a bowl; gently fold mixture with a wooden spoon until blended, 3 to 5 minutes. Pour mixture into bottom pie crust and cover with top crust. Seal the edges; make slits in the top with a sharp knife.

Refrigerate pie until sealed edges appear firm, 10 to 20 minutes.

Bake pie in the preheated oven for 15 minutes. Reduce oven temperature to 350 degrees F (175 degrees C), and continue baking until crust is golden brown, about 30 minutes.