Mighty does not yet smoothly allow users to drag and drop tabs from one window into a new or existing window. We know that this is a very common productivity workflow for many of our users and it's on our list of things to improve on.
For now, one alternative method of doing this is to right-click on a given tab > Move tab to a new window. This should reduce momentary "gray screens" and/or choppiness when separating or combining tabs into new windows.
Please let us know if this is a very important workflow for you so that we can email you directly when we make progress on this!