Melt butter in medium saucepan over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook until fragrant, about 30 seconds.
Add tomato sauce, cherries, brown sugar, orange juice, molasses, cider vinegar, ancho chili powder, mustard, salt, white pepper, and cayenne and stir to combine. Bring to a boil, then reduce heat to low and simmer until slightly thickened, about 30 minutes, stirring occasionally.
Transfer sauce to the jar of a blender and blend until smooth. Let cool to room temperature, transfer to a jar and store in refrigerator for up to a month.