If I’m understanding correctly, you want to have the blog feed only show specific categories correct? This would be the same thing as picking out individual posts not to show since you could just put them in their own specific category.
What you will need to do is NOT use the main Theme Options to select the page to display your blog. Instead, you will create a Template with the Template Builder to show a customized blog layout.
Create a new Template then add a Blog element to that template. Select the categories you want to appear and then save it. Next, you’ll assign the “Blog” template to the page of your choice and title it as Blog and add it to your main menu using the Appearance>Menus area.