To mix multiple Joomla Categories by Article date make sure the Menu item setting "Category Order' is set to "No Order".
Otherwise the articles will be displayed sequentially by Category order and not mixed by Article date.
The subcategories need to be nested under the Category that will be shown in Blog format (in the Category Manager).
The image below shows the settings for the Menu item (menu type Blog Category) that will link to the parent Category.
- "Category Order" set to "No Order".
- "Include Subcategories" set to "All"
- "Article Order" will probably be "Most Recent First" (depends on your preference).
- "Date for Ordering" will probably be 'Published" (depends on your preference).