(( jan ))
Wrap or tie or rubber band an old towel around the broken mop. Spray the floor with cleaner---all purpose cleaner, window cleaner, bath tub cleaner, shampoo---doesn't matter, it's all soap and water

... or just push an old towel around with the broken mop. Or throw some paper towels down in place of the towel and push them around the sprayed floor.
Then turn on some music that will help you feel energetic.
Plan a reward for yourself afterward! Food? Nap? Time to enjoy some reading? Order a mop online?