To install this script you will need a userscript plugin, I recommend Violentmonkey.
After installing the plugin, simply visit this link and it will propmpt to install the userscript.
On the navigation bar on the left side of twitter you will see a new mute icon appear, clicking it will display a modal where you can list the usernames you wish to mute. The usernames are Case Sensitive, and should be listed one per line, without the @. Upon closing the modal, either through the × or by clicking the icon again, the mute will take place. However, if you remove a name you will have to refresh the page to see their content in your home again.
This mute feature will remove all content from the users in the list from your home feed, including posts, likes, posts mentioning them, etc, but it will allow you to see them anywhere that isn't your home feed, and you will recieve notifications from them as normal. This is useful if you want to still interact with someone, but don't wish to see their content.