"You think you can kill me?"
Firstly you should note (since it's not in your translations) that 殺せる is "can kill" / "to be able to kill" (this is the ～える godan potential form).
With potential constructions and certain verbs like 見える and 分かる, the thing that we would think of as the object in English is often marked by が instead in Japanese. What would be the subject is then marked with に.
I can't hear high frequencies any more.
( -- space alc - 英辞郎)
(I think "High-frequency sounds do not render (themselves) audible to me." might be somewhat close to the grammar of the Japanese...?)
Potentials work the same way, so the に in
is referring to the person who is able / not able to do 殺す.
The subject of 思ってる is also "you", but that is not explicitly mentioned in the sentence (i.e. this お前 noun is not the explicit subject of 思ってる).
In general it'd be a bit unusual for 私 to be the subject of 「思ってるのか？」 unless you're talking to yourself...
This isn't the only way to use particles with these verbs... the normal form of が and を is also possible as far as I know... that's probably best kept for another question (or perhaps it has already been covered).