Can I say this sentence in Japanese, or does it makes no sense then?
I want to say the weird sentence "You're killing me with your cuteness" in Japanese.
But does this sentence even make sense in the Japanese language?
Moreover: How do I translate this?
"貴女のキュートは私を危めます"??? Maybe something like that?
(My Japanese is really bad, I know. Sorry for that. :

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Answer

I agree kei-san. 
Although "貴女のキュートは私を危めます" is not very natural , but it makes sense.  At least I'd understand if someone happens to say so to me.

The more natural way to say what you mean is:
○○さんがかわいすぎて、（私は）死にそうです。

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Some of the reasons your original sentence is not natural:
1) キュート is  an adjective, not a noun. So you can't really say キュートは・・・。
2) The verb 危めます is not commonly used.

Answer

No I think ok because this is enphasis of cuteness.Japanese sometime we set enphsis word came first and explanation later therefore ( 君のキュウトは!! 私を危めます）is all right. but this is speaking langage
 but put Into Japanese :  貴女は綺麗過ぎる．
 but your Japanese may be make sense to Japanese