Do I clean off the old ointment before applying new ointment around cotton ball and over the stitches?

You should follow your doctor's wound care instructions, which vary from doctor to doctor. I'm disappointed that your doctor used a skin graft in this location, as this area heals beautifully if left to heal by itself, leaving a result that looks like nothing was ever done. The graft, if it even takes, will always look like skin from somewhere else. But, as one doctor once told me, "I don't get paid for letting it heal by itself". 

Unless directed by your surgeon, I would leave the dressing alone so that you do not disturb the graft.  I would wait for him/her to remove it and reapply a fresh bandage.  You may clean the crust around the edge with a solution of soap and water, and using a Q-tip, dip it in the solution to remove the crust.  Take care to not disrupt the graft or the dressing over the graft, since it is important to allow it to cement on to the wound bed for the 1st two weeks. If the dressing is off the graft, then I would reapply fresh ointment on the wound and rebandage.