Tounge Twisters are a great way of warming your voice and mouth up before performing. Try speaking these faster and faster, and sing some of them too. If you over-exaggerate your mouth shape when doing these too, that will help with moving your mouth when singing.
she stood upon the balcony inexplicably mimicking him hiccoughing and amicably welcoming him in.
A flea and a fly flew up in a flue.
Said the flea, "Let us fly!"
Said the fly, "Let us flee!"
So they flew through a flaw in the flue.