I came across this sentence in my JLPT mock test book:
I don't understand what kind of grammar and what is the meaning of the bold phrase. It looks like an expression.
It's a phrase to express "despite doing it over and over". You can use it with other verbs e.g. 食べても食べてもお腹がいっぱいにならない、拭いても拭いても落ちない etc
Unless it's an expression that I've never heard before, it just sounds like a straight-forward, emphatically figurative translation.
In my life right now, (I'm) overflowing/inundated with things; (such that) even if I throw them away [twice for emphasis], they continue increasing.