Learn Turkish: Kutu mutu atacağımızı biliyorsun. - You know that we will throw away boxes and stuff.

Kutu means "box". By repeating the word and replacing the first consonant with an m, you get kutu mutu, which translates to "boxes and stuff" or "boxes and things like that". It is a handy way to refer to a vague, general category based on the original noun.

Since kutu mutu is the thing being thrown away, why doesn't it have an accusative case ending (like kutuyu mutuyu)?

Because it acts as an indefinite object here. You are not talking about throwing away the specific boxes, but rather the general concept of "boxes and stuff". General, indefinite direct objects usually sit right before the verb and do not take the accusative case suffix.

Can you break down the suffixes attached to atacağımızı?

Certainly! This is a noun clause acting as the object of "you know". It starts with the verb root at- (throw), followed by the future participle -acak (which softens to -acağ- due to vowel harmony). Then we add the first-person plural possessive -ımız (literally "our future throwing"), and finally the accusative -ı. The accusative is required because this entire clause is the specific, definite thing that "you know".

Is it acceptable to use forms like kutu mutu in formal writing?

No, this type of m- reduplication is highly colloquial. While it is incredibly common and natural in everyday spoken Turkish, it sounds out of place in formal documents, academic writing, or professional emails.