Peel blood oranges and cut away the white pith, then cut orange segments between membranes; roughly chop and set aside.
Place cranberries, sugar, cider vinegar and allspice in a large bowl; place half of mixture in food processor and pulse until roughly chopped. Remove to serving bowl. Repeat with remaining half of cranberry mixture, adding to mixture in serving bowl. Add pearl onions, thawed to room temperature, to food processor and pulse 2 to 3 times or until very roughly chopped. Add to mixture in serving bowl and stir in chopped blood oranges.