Correct spelling, explanation: the word suppresses is the third person singular verb. It originates from the Latin suppress. As you can see, the etymology indicates that the second consonant in this verb should be doubled. If you’re not sure how to spell a word, always look at its history, because it can be very helpful. Suppresses is the only correct version and supresses is just a mistake.

Definition of suppresses:
verb (third person), forcibly put an end to
The dictator tried to suppress all criticism of him.
The army acted swiftly to suppress the uprising.

Collocations with suppresses::
Some most commonly used collocations include: suppress rebellion and suppress anger.
King Robert had to suppress the rebellion to keep the throne.
It is not healthy to suppress your anger. You need to learn how to control it.

Incorrect spelling, explanation: the form supresses is not correct because it does not accord with its word formation base: the verb suppress. So, it should be spelled with a double -p and a double -s. None of them can be forgotten. This mistake can be made due to a large number of consonants in one word. But remember to always look at the root. Suppresses is the only correct spelling.