When an online account is closed for good, “fermé” is the most appropriate word; “supprimé” (albeit not entirely wrong) is usually more about a video being removed, deleted. “Clôturer” is used more formally (as an antonym of “ouvrir”) when you close, for instance, a bank account.

A YouTuber explaining the reason for the closure of his account:

« Pourquoi cette chaîne est-elle fermée ? »

“Fermé” conveys the idea of an account being closed permanently:

Le compte Twitter de Donald Trump a été fermé.

With “supprimé / coupé / désactivé”, on the other hand, an account may be closed only temporarily (accidentally or otherwise), with “désactivé” especially emphasising this temporary nature:

{vs}: Le compte Twitter de Donald Trump a été supprimé / coupé / désactivé.

As a French, I think that “supprimer” is the best word for this situation because the account is completely removed, with its user data.
The word “fermer” can be used too, but I think it can be confusing if you say “Je ferme mon compte” because sometimes you could understand that you close your account without being sure that the data is removed. Notice that if your account is closed by the administrator of the website, you would more likely use “Mon compte a été fermé” because you haven’t decided to close your account.
The word “clôturer” is, like @Alone-zee mentionned, when you close a bank account.

Example:

J’ai supprimé mon compte.

In this situation, I am sure that my account has been deleted.

Mon compte a été fermé par les administrateurs du site.

In this situation, my account has been closed by the websites administrators.

J’ai fermé mon compte.

It can also be used in the case that the user closed his account, but it is not used very often.

J’ai clôturé mon compte.

It is used when you close a bank account.

If you want to close you account temporarily, or if it has been shutdown temporarily by the administrators, you would use the word désactivé

Mon compte a été désactivé par les administrateurs