Yoshi is canonically a dinosaur. Dinosaurs had cloacas and laid eggs.
This means they just fire eggs out of the same place they shit from.
This also means every time Yoshi engulfs a character in Super Smash Bros, they're basically shitting the player out after encapsulating them.
The Vulpine Club is a friendly and welcoming community of foxes and their associates, friends, and fans! =^^=