No me tires esta revista.

I think “no me tires” here means “don’t throw at me” not “don’t throw away”.

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I think both interpretations are possible.

Interesting. What purpose does “me” serve in the sentence if you interpret the meaning as “don’t throw away”?

Okay, the translation does not involve “me”. I meant, it could be interpreted as “Don’t throw the magazine away for me”.