After digging around, I finally found this relatively simple pre-save hook on the Jupyter docs. It strips the cell output data. You have to paste it into the jupyter_notebook_config.py file (see below for instructions).

def scrub_output_pre_save(model, **kwargs):
    """scrub output before saving notebooks"""
    # only run on notebooks
    if model['type'] != 'notebook':
        return
    # only run on nbformat v4
    if model['content']['nbformat'] != 4:
        return

    for cell in model['content']['cells']:
        if cell['cell_type'] != 'code':
            continue
        cell['outputs'] = []
        cell['execution_count'] = None

c.FileContentsManager.pre_save_hook = scrub_output_pre_save

From Rich Signell's answer:

If you aren't sure in which directory to find your jupyter_notebook_config.py file, you can type jupyter --config-dir [into command prompt/terminal], and if you don't find the file there, you can create it by typing jupyter notebook --generate-config.

After digging around, I finally found this relatively simple pre-save hook on the Jupyter docs. It strips the cell output data. You have to paste it into the jupyter_notebook_config.py file (see below for instructions).

def scrub_output_pre_save(model, **kwargs):
    """scrub output before saving notebooks"""
    # only run on notebooks
    if model['type'] != 'notebook':
        return
    # only run on nbformat v4
    if model['content']['nbformat'] != 4:
        return

    for cell in model['content']['cells']:
        if cell['cell_type'] != 'code':
            continue
        cell['outputs'] = []
        cell['execution_count'] = None
        # Added by binaryfunt:
        if 'collapsed' in cell['metadata']:
            cell['metadata'].pop('collapsed', 0)

c.FileContentsManager.pre_save_hook = scrub_output_pre_save

From Rich Signell's answer:

If you aren't sure in which directory to find your jupyter_notebook_config.py file, you can type jupyter --config-dir [into command prompt/terminal], and if you don't find the file there, you can create it by typing jupyter notebook --generate-config.