Learn German: Wo ist mein Handtuch? Ich finde meins nicht. - Where is my towel? I cannot find mine.

In the first sentence, mein sits right next to the noun it describes (mein Handtuch). But in the second sentence, the word stands alone to mean mine. When a possessive word replaces a neuter noun (like das Handtuch) entirely, it gets an -s ending, making it meins (or meines).

Is meins in the accusative case here?

Yes. Because it is the thing you are trying to find, it is the direct object of the verb finden, which requires the accusative case. For neuter nouns, the accusative form is identical to the nominative form, which is why it stays meins.

What would the sentence look like if I was looking for a masculine noun, like der Pullover?

You would need the masculine accusative ending for the standalone pronoun, which is -en. The sentence would be: Wo ist mein Pullover? Ich finde meinen nicht.

Why does the negation word nicht go at the very end?

When you negate an entire action (like not being able to find something) and the direct object is a specific pronoun like meins, the word nicht is pushed to the very end of the clause.