Translation:I do not want you to hurt yourself.
This seems a little odd to me. Why does "ska" need to be in the sentence. Wouldn't "Jag vill inte att du skada dig" suffice?
The sentence doesn't work unless you use "skada" in the present tense "skadar".
skada is the infinitive form, and you can't just use a bare infinitive with a subject, you never do in English either. (You don't notice the difference so much in English since your infinitive is often the same form as the present.)
Here, you have the construction want someone to do something. In Swedish, it's not possible to vilja någon att göra något, our counterpart is jag vill att någon ska göra något or jag vill att någon gör något.
In that case, which is more common? > Jag vill inte att du ska skada dig or > Jag vill inte att du skadar dig ? I'm guessing the first sentence is a warning for something that might happen later in the day/week/year, whereas the second sentence is something you'd say if someone was going to go do something dangerous a few minutes later...
I did some searches and they seem to be about as common, but ska has a stronger sense of future to it. I also have a feeling that ska is what is traditionally considered correct here, but the plain present tense is getting more common.