What can I mix with a sweet liquor to cut its sweetness?
Add a splash to hot coffee for a fabulous liquor coffee, or use with cold brewed coffee in a Tiramisu dessert. Adding fat (i.e. mascarpone) and bitterness (i.e. coffee) or sourness (i.e. citrus suggested in first answer, or natural yoghurt) will help balance the sweetness.  Also chilling sweet food and drink reduces their detectable sweetness - perhaps make an alcoholic sorbet or frappe.