Can you exclude a category of posts from showing on the main blog page?

I know you can target blog categories in the code for additional styling, but can you stop a specific category from showing up on the main blog (list) page?

I'd like to add a collection of posts, to be accessible only from it's category page url, and not with all the others. I know I could create a second blog and style that to match, but excluding a category sounds like it would be easier to manage and open up other potentials.

Anyone know if this is possible or anything I could look into to try?

Technically the answer is no, but you can do a workaround. 

If you use summary blocks on a page or in a second blog or as a post in the blog you have.   By filtering a category or simply making the block look for featured posts and any post that doesn'have featured turned on will not show up in the list. I use category links in folders as well to seperate certain groups of posts from all the others. 

In your case you make a summary block looking for featured posts, and don' t turn that on for any others. Those posts can have their own page, on the nave bar if you wish. I use this technique on my site a lot, my main blog is in the unlinked section of my site. 

You can see it in action here:

https://myrandomviews.com/blogsummary