Using iCloud Storage to backup data
You can use iCloud either to backup your iDevices' data and also as storage for your personal files, just like those saved in your HDDs disk.

Where?

As you said, instead of saving those files in your iCloud folder in your Mac, you can go to the iCloud website and login with your own Apple ID credentials.

How?

After you've logged in to your iCloud space, you'll get to the main screen where you can see all the Apps you can launch directly on the website (Photos, Numbers, Keynote, etc..).
You'll want to launch the iCloud Drive app, and once in it you should see 5 buttons on the top of the page.

The button you're looking for is the second starting from the left: the Upload button.
It will pop up a window where you can browse your entire File System with, and search for the files you want to upload to your very personal iCloud Drive.
After you chose the files, it will start automatically to upload them up in the cloud. Once done, feel free to delete those files from your Mac/Computer and access them whenever you wish, directly from your iCloud Drive App, which can be found either on the website we've just talked about, or even inside your iDevice.

If you haven't activated it yet on your iDevice, simply do the following:


Open Settings
go to the iCloud tab
Find the iCloud Drive option and switch it to ON.


You now have the App visible and accessible directly from the Home screen of your iDevice!

Note!

You're free to use iCloud as a storage solution, but I feel like you should remember by default you get 5GB for free on iCloud, if you want to upgrade your storage capacity, you'll have to pick a storage plan. At the moment there are 3 optional plans for iCloud storage:


50GB
200GB
1TB


The price will vary depending your location, you can check this article from the Apple Support website to find your own location's prices.