Good explanation by @vkareh and @mazinger. I'm a Brit fluent only in English and American (lived in USA for ~ half my life), but now struggling to learn Spanish as a 2nd/3rd language.
To clarify that sentence for non-Spanish speakers from my non-Spanish speaking viewpoint: IIUIC once you know that mate is a Spanish word you'd only pronounce it as @mazinger said: 'mah-teh' (or maah-teh, because for simple 2-syllable words like mate the default rule is always to stress the penultimate vowel, hence the 'a' is stressed (longer) vowel anyway so it never needs an accent mark on it. The accents in Spanish are only used when some other vowel - instead of the default one - needs to be the accented one, like the maté example ('ma-tay' - translation 'I killed').
Note I said for 2-syllable words. Once you get to more than 2 it gets very complicated very quickly, because the rules, like most of Spanish spelling/pronunciation rules, are very consistent (compared to say English) and depending on the relative position of the syllable in the word, but ... numbered from the end backwards towards the front. A little subtly that they never tell you in Spanish class because, well, it's just a natural way in Spanish.
And @mazinger 's reference to 'an accent mark or tilde" is interesting too. When he says tilde we English speakers just think of the symbol also used to mean approximately as in ~2. But tilde in Spanish, as I understand it, means an accented letter, any accent not just the ~= one. This nugget of confusion was caused by the English language, which when faced with needing to name that Spanish accent which didn't exist in English went "Well it's a Spanish accent, and they call accents tidle, so we'll just call it that!". Not too helpful