der, die oder das Mutter?

Exception

-er → der

Usually 81.3% of the 2,315 common nouns ending in -er take der.

Mutter breaks this rule: it is die Mutter, not der Mutter.

This is only a tendency. Common exceptions are family words (die Mutter, die Tochter) and das Zimmer, das Fenster.

Other exceptions die Tochter, die Schwester, das Wasser, das Alter