To be honest the answer is very obviously no and here is why…
The time paradox, butterfly effect, whatever you want to call it it’ll happen.
How could you exist to kill yourself if you travel back in time to kill yourself? A future you would not exist if you kill a past you therefore a past you will have never lead the life it did to get to where you are now to kill yourself.
From what I believe of a time paradox the actual event of killing your past self can physically be done but it would then alter everything and in reality it would just never have happened because unlike a world where you swing back in time to have sex with your mum and create yourself this is a act that can only be done once and once it is done you are replaced with someone else leading a different line.
I guess then the answer actually is yes BUT its bloody stupid and you could end up making the world implode if you did.