See this SO answer: https://stackoverflow.com/a/34583288/2476920
Personally, I love to have notebook cells to be able to code without re-running everything. Especially in the case of deep learning, training a model is long. Jupyter is very good for creating and debugging code that: A) needs a trained model loaded for it to work but you want to skip the part of saving/loading the model, or B) code that saves-then-load a model.
If the "mutable state with global variables" drives you crazy, you may want to avoid reusing the same variable names from one cell to another, and reset the notebook more often. Also, avoid side effects (such as writing/loading from disks) and try to have what's called pure functions (e.g.: avoid singletons or service locators, pass references instead). If your code is clean and does not do too much side effects, you should be able to work fine in notebooks without having headaches.
EDIT: typo.