Generally this is possible as it is a common Android feature. I can speak for Lollipop and Marshmallow (depending here on if your sd card is used/formated as internal or external memory).
Your app info at settings->apps->whatsapp should show if moving to sd card is possible for this app or not. If the button “move to sd card” is active you may move the app to the sd card and back again if you like. If it´s greyed out it won´t work. Just for validation also look into the app info of other apps for this button to be active. If you cannot find any with active button then maybe (for Marshmallow) you have your sd card in use as internal memory.
But as I am not on whatsapp I cannot tell you for sure if it will let you move it to the sd card. Also it´s not sure if it then will automatically save its entire data in the same memory area which keeps the app. Therefore I again would expect an app specific setting maybe.