A coffee press grounds removal apparatus for removing coffee grounds or tea leaves from a coffee press machine is provided. The coffee press machine has a plunger apparatus for pressing the coffee grounds or tea leaves within a carafe. The apparatus comprises a basket receivable within the carafe with the basket having an open top, a bottom wall, and a side wall extending in a generally upward direction from the bottom wall toward the open top. A handle is pivotally connected to the basket wherein the basket is completely receivable within the carafe. The basket comprises a configuration substantially mirroring the interior circumference and shape of the carafe in which the basket is seatable wherein as the basket is inserted into the carafe, the basket slidably engages the interior circumference of the carafe such that an outer surface of the side wall of the basket contacts the interior circumference of the carafe. The entire bottom wall contacts a bottom surface within the carafe with the bottom wall sandwiched between the coffee grounds or tea leaves and the bottom surface and the plunger apparatus pressable against the coffee grounds or tea leaves.