There is nothing wrong with breaking up a single verse over two rak‘ahs, but that is contrary to what is preferable
Question

                In Taraweeh prayer, the imam used to recite the verse on debt in Soorat al-Baqarah, but he recited it over four rak‘ahs, breaking it into several parts.

Is that permissible?
Praise be to Allah.
    It is permissible for the worshipper, after reciting 
    al-Faatihah, to recite part of a verse, especially the lengthy verses such 
    as the verse on debt. There is nothing wrong with breaking it up and 
    reciting it over two rak‘ahs. There are several texts which indicate that. 

    Firstly: 

    All of the Noble Qur’an is the word of Allah, may He be 
    exalted, and in all of its sentences and words there is reward and virtue. 
    Whoever recites a few words of it, or some verses, has recited something of 
    the words of Allah, may He be exalted, and will attain the reward for that, 
    by Allah’s leave. Allah, may He be exalted, says (interpretation of the 
    meaning):

    “So, recite of 
    the Quran as much as may be easy for you”

    [al-Muzzammil 73:20]. 

    It was narrated that ‘Abdullah ibn Mas‘ood (may Allah be 
    pleased with him) said: The Messenger of Allah (blessings and peace of Allah 
    be upon him) said: “Whoever reads 
    one letter of the Book of Allah will have one hasanah for it, and each 
    hasanah is a tenfold reward. I do not say that alif-laam-meem is a letter, 
    rather alif is a letter, laam is a letter and meem is a letter.”

    Narrated and classed as saheeh hasan 
    ghareeb by at-Tirmidhi; classed as saheeh by al-Albaani in Saheeh at-Tirmidhi. 

    Secondly: 

    Many verses include a number of complete and independent 
    meanings, which makes each one of them suitable to be recited and reflected 
    upon by itself, such as the verse in which Allah, may He be exalted, says 
    (interpretation of the meaning):

    “So unto this 
    (religion of Islam, alone and this Quran) then invite (people) (O Muhammad 
    SAW), and Istaqim ((i.e. stand firm and straight on Islamic Monotheism by 
    performing all that is ordained by Allah (good deeds, etc.), and by 
    abstaining from all that is forbidden by Allah (sins and evil deeds, etc.)), 
    as you are commanded, and follow not their desires but say: "I believe in 
    whatsoever Allah has sent down of the Book (all the holy Books, this Quran 
    and the Books of the old from the Taurat (Torah), or the Injeel (Gospel) or 
    the Pages of Ibrahim (Abraham)) and I am commanded to do justice among you, 
    Allah is our Lord and your Lord. For us our deeds and for you your deeds. 
    There is no dispute between us and you. Allah will assemble us (all), and to 
    Him is the final return”

    [ash-Shoora 42:15].

    So if a person recites part of this verse with a complete 
    meaning, for example, there is nothing wrong with that. 

    Thirdly: 

    There is no report of any prohibition on breaking up a single 
    verse or even on breaking up a single soorah. As no such prohibition has 
    been narrated, and the general basic principle indicates that it is 
    permissible, the ruling on that is that which is indicated by the general 
    basic principle. 

    Fourthly: 

    In the words of the fuqaha’ we find that which also clearly 
    indicates that this is permissible. 

    Ibn al-Hammaam al-Hanafi (may Allah have mercy on him) said: 

    If he recites half of a lengthy verse such as Aayat al-Kursiy 
    or the verse on debt, it was said that it is not permissible because it is 
    not a complete verse, but the majority (of scholars) are of the view that it 
    is permissible… This was stated definitively by al-Qadoori, who said: The 
    correct view according to the madhhab of Abu Haneefah (may Allah have mercy 
    on him) is that whatever may be called Qur’an is permissible. This is also 
    the view of Ibn ‘Abbaas, who said: Recite whatever you have learned of 
    Qur’an, and nothing of the Qur’an can be regarded as too little. 

    End quote from Fath al-Qadeer, 1/333 

    An-Nafraawi al-Maaliki (may Allah have mercy on him) said: 
    After reciting al-Faatihah, you may recite – as it is Sunnah – something 
    from the Qur’an, even if it is a short verse, such as “With spreading 
    branches” [ar-Rahmaan 55:48] and  “Dark green (in colour)” 
    [ar-Rahmaan 55:64], or part of a lengthy verse such as the verse of 
    debt. But it is preferable to recite a complete soorah. 

    See: al-Fawaakih ad-Dawaani, 1/178; Haashiyat 
    ad-Dasooqi, 1/242 

    Ibn Hajar al-Haytami (may Allah have mercy on him) said: 

    One may attain the Sunnah action with less than a verse.

    End quote from al-Minhaaj al-Qaweem Sharh al-Muqaddimah 
    al-Hadramiyyah, p. 99 

    Al-Bujayrimi ash-Shaafa‘i (may Allah have mercy on him) 
    said: 

    If he recites part of a verse, he will have attained the 
    Sunnah action, and that is acceptable if it conveys a complete meaning, such 
    as a short verse that gives a complete meaning.

    End quote from Tuhfat al-Habeeb ‘ala Sharh al-Khateeb, 
    2/68 

    Al-Mardaawi al-Hanbali (may Allah have mercy on him) said: 

    The correct view is that reciting a soorah after al-Faatihah 
    in the first two rak‘ahs is Sunnah. This is the view of our companions… It 
    says in al-Furoo‘: What appears to be the case is that even part of a 
    verse (is sufficient), because of the apparent meaning of the report.

    End quote from al-Insaaf, 2/120 

    Fifthly: 

    However, we say that this action is contrary to what is 
    preferable, because a single verse is discussing one topic, and the words of 
    this verse are interconnected, so breaking it up usually leads to an 
    incomplete meaning and damaging the context. Hence the early generations 
    regarded it as mustahabb (preferable) to recite a complete soorah, and to 
    avoid breaking it up in more than one rak‘ah. So it is more apt to say that 
    this is also preferable with regard to a single verse, even if it is 
    lengthy. It says in the saheeh hadeeth – about the story of the Ansaari who 
    was struck by an arrow (shot by a mushrik) when he was praying –: When the 
    Muhaajiri saw the blood of the Ansaari, he said: Subhaan Allah! Why did you 
    not alert me the first time he shot (the arrow)? He said: I was reciting a 
    soorah and I did not want to interrupt it.

    Narrated by Abu Dawood in as-Sunan, 198; classed as saheeh by 
    al-Albaani in Saheeh Abi Dawood. 

    It was narrated that ‘Abdullah ibn Mas‘ood (may Allah be 
    pleased with him) said: Give each soorah its due of focus of mind and 
    humility. Narrated by Ibn Abi Shaybah in al-Musannaf, 1/324 

    Hence Ibn al-Qayyim said:

    It was the practice of (the Prophet (blessings and peace of 
    Allah be upon him)) to recite a soorah in full, or sometimes he would recite 
    it over two rak‘ahs, or he would recite the beginning of the soorah. With 
    regard to reciting the last few verses of a soorah, or verses from the 
    middle of it, that was not narrated from him.  

    End quote from Zaad al-Ma‘aad, 1/208 

    And Allah knows best.