The actual blood is blood, there is actually fairly little blood, most of what you see is endometrial lining.
this is the soft lining that builds up ready for a fertilised egg to implant into if you become pregnant.
As this thin layer is shed the uterus contracts to help shed it - this is part of the cramping.
the uterus is a muscle and as it contracts it cramps.
as the lining and blood pass through the cervix the cervix will often contract and release - which is another source of cramping.
It is common to feel cervical cramps when passing clots.
Many women find the surrounding muscles also cramp - ie their abdomen, back, thighs.
It's not likely that you'd feel pain in your ovaries at this time - more like achy, cramping in the general pelvic area.