Your poor dd. And horrendous to think that a playground supervisor would be so dismissive of such injuries and behaviour inflicted on your dd.
I would go to the doctor's tomorrow to get it in her records and check there's no infection in the wounds, before going to school.
I would then speak with the HT as an urgent matter so that she can deal with it immediately and so that she can see your dd's back and blood stained top, and make sure that this girl and the PS are kept away from your dd in the immediate future. I would also let her know that I will be following up the meeting with a formal complaint in writing, but emphasize that you felt you needed to talk to the HT before your dd returned to classes because you couldn't possibly let your dd return without knowing that she would not be injured or bullied again before the HT had a chance to read your letter. Make sure that you say that you are holding the HT personally responsible for the safety of your dd. Think before you go in of what sort of measures would make you feel that your dd is safe - eg if the child was older then you would hope that they were excluded for a few days, as well as kept away, or moved to a different class. Not sure what they can do when they are 6 - but the pass mentioned earlier sounds a good idea and there might be other things. If you go in asking for several things, they might be able to do some but not all so ask for more than you want in order to have room to negotiate and still end up with what you want!
When you do write the letter, make sure it gets sent to the governors and the local education department - I guess their welfare officer but if you call them up they will be able to tell you the right person to send it to. I would also be prepared to say that if they can't guarantee my dd's immediate safety whilst in school currently then you can't leave her there until they can - and be prepared to go home with your dd - telling them that you will take home work with you, and that it had better be put down as authorised absence or you will be raising merry hell about that too.
For a 6 yr old to be repeatedly scraping a stick hard enough down another child's back to draw blood - and going to the trouble of lifting up her clothes in order to do it - doesn't sound like normal 6 yr old behaviour - maybe a nasty kid would poke with a stick but going this far? I wonder if she has been a victim of something herself and this is a red flag that should be used to investigate her? Not saying she doesn't need telling off - but alongside this she needs to be dealt with to find out why she would think of doing this and if she has experienced something similar or seen others do it.
I would also be tempted to report to the police - not that you expect them to do anything as she is so young, but it would then be on record. But even a chat from a policeman might make her realise (and her parents if they are not aware of her behaviour) quite how far over the line she went and that what she did was a very very naughty thing that should never be repeated. And maybe they could send round a community policeman to do a session for everyone on how to treat others, not to hurt them etc because that's a bad thing to do and will get them into trouble.
How well does your dd get on with her class teacher normally? I would also talk to her - not to get her to punish the other child or deal with the PS, but to make sure that your dd gets looked after in class and the bully is kept away from her at all times. And to reassure her that regardless of whatever anyone else says, she isn't a baby, she is very brave because she has all her injections which is much braver than most of teh others in the class, and that she can feel free to come to talk to her at any time, especially if she is in pain. Could you and the teacher also say to your dd that because of her diabetes that even if it is only a little bit of blood or soreness (and even if a teacher or another pupil have said something silly or nasty to her) that it is still important that she tells the teacher about it so she can make sure she is OK - ie something that effectively gives her the OK in her mind to talk to her teacher even if another one has told her that she doesn't need to. If this scenario were then to play out identically for a second time (hoping to goodness it doesn't!) this would then hopefully give your dd the confidence to talk to her teacher about her injuries rather than sitting there thinking that she couldn't talk to her because the PS had told her she was a baby and that there was nothing wrong with her.
If your dd is in pain or if the doc gives her something to treat her back, I would make sure that your dd tries to take at least one dose in school, so they can see that your dd has been so badly hurt in their care that she needs medication.
Sorry, all a bit of a jumble. But really hope that your dd is OK and the school deal with this properly for you.