So you want to clear the cache for just one site in the FireFox browser, but without losing all the other sites you visited. And yes, you want the one site cleared from the cache, not just the history. No problem - there's a very easy way to do that. Here's how:
Step 1 of 2: Get into your FireFox history
First of all, go to your FireFox history. There's an easy shortcut, by the way: when you open FireFox, press Ctrl-H and it'll take you to your history. Your screen should now look like the image below:
Step 2 of 2: Look for the site you want to clear from the cache
In case it's hard to find the site among all the other things in your browsing history, use either the search box (circled in the pic above), or the View options that change the order of what you see there (also circled above).
Once you see the site that you want to delete from the cache, simply right-click on its name. A new menu will come up and in that menu, go to "Forget About This Site" and left-click on it, as shown in the image below. That's it! You're done! Now that site has been cleared from both the browser cache and the history.
Yes it is possible to clear the cache for just one site in the FireFox browser, allowing the browser to "forget" about that site, while still remembering all your other sites. It's an easy two step process as shown above, and after doing it, that specific site is removed from your cache, but not other sites you visited.
This is ideal when you are trying to do a precise removal of one site, without removing all the sites from your cache.