There are a few opinions in the Islamic tradition regarding the number of times the trumpet will be blown.
Some say that there are three: nafhkat al-fazaʿ (fright), nafkhat al-ṣaʿaq (death), and nafkhat al-baʿth (resurrection). They state that the first is proven through Verse 87 of Sūrah al-Naml:
وَيَوْمَ يُنفَخُ فِى ٱلصُّورِ فَفَزِعَ مَن فِى ٱلسَّمَـٰوَٰتِ وَمَن فِى ٱلْأَرْضِ إِلَّا مَن شَآءَ ٱللَّه
And (remember) the day when the Trumpet will be blown; so all those in the heavens and the earth will be in panic, except those whom Allah wills.
According to them, the latter two are established by Verse 68 of Sūrah al-Zumar:
وَنُفِخَ فِى ٱلصُّورِ فَصَعِقَ مَن فِى ٱلسَّمَـٰوَٰتِ وَمَن فِى ٱلْأَرْضِ إِلَّا مَن شَآءَ ٱللَّهُ ثُمَّ نُفِخَ فِيهِ أُخْرَىٰ فَإِذَا هُمْ قِيَامٌۭ يَنظُرُونَ
And the Trumpet will be blown, and all those in the heavens and all those in the earth will fall dead, except those whom Allah wills (otherwise). Thereafter, it will be blown once again, and they will rise up at once, looking around.
Ibn Kathīr also concurs. In addition, he mentions that the nafhkat al-fazaʿ is alluded to in Verse 49 of Sūrah Yā Sīn:
مَا يَنظُرُونَ إِلَّا صَيْحَةًۭ وَٰحِدَةًۭ تَأْخُذُهُمْ وَهُمْ يَخِصِّمُونَ
They are awaiting nothing but a single blast that will seize them while they will be quarreling.
He adds that the nafkhat al-baʿth is mentioned in Verse 51 and that the nafkhat al-ṣaʿaq occurs between it and the nafhkat al-fazaʿ:
وَنُفِخَ فِى ٱلصُّورِ فَإِذَا هُم مِّنَ ٱلْأَجْدَاثِ إِلَىٰ رَبِّهِمْ يَنسِلُونَ
The Trumpet will be blown, then — behold! — they will rush from the graves to their Lord.
Some others who hold this opinion are Imām al-Samarqandī, Imām al-Thaʿlabī, Imām Makkī b. Abī Ṭālib, and Imām Ibn al-ʿArabī.
Others mention that there are only two blowings of the trumpet. Some who are of this opinion are Imām Ibn Abī Zamanayn, Imām al-Māwardī, Imām al-Baghawī, Imām al-Bayḍāwī, Imām Abū Ḥayyān, Imām al-Maḥallī, Imām al-Suyūṭī, and Imām Abū Saʿūd . Additionally, Imām al-Qurṭubī mentions in al-Tadhkirah bi Aḥwāl al-Mawtā wa Umūr al-Ākhirah that the nafhkat al-fazaʿ and nafkhat al-ṣaʿaq are one and the same, as there is istihnāʾ in mention of both (al-Naml 87 and al-Zumar 68). Also, the famous ḥadīth mentions there are 40 between the two nafkhahs of the trumpet. Furthermore, Imām al-Rāzī says that ثُمَّ in Verse 68 of Sūrah al-Zumar indicates that it is referring to the first nafkhah.
In conclusion, both opinions have their respective proofs and are supported by great scholars.