First of all, ensure you're using the right mug. Glass, ceramic, and some plastics are typically suitable for microwave cooking, but check the mug you're using is labeled as being safe for the microwave. As for removing the finished carrot mug cake, run a knife around the outside of the mug and then turn it out onto a plate or into a bowl. It might come out looking a bit lopsided, but that won't affect the flavor. You can also just eat it straight out of the mug which is what I like to do.