I am writing a story and want to portray one of the characters as harmful and abusive. I was wondering if I am allowed to have him use vulgar words because it is not me saying it, it is him.
I cannot think of any reason why this would be impermissible when there's clearly no intention of wrongdoing. The Prophet (peace be upon him) said that actions are judged by their intentions. I think people need to avoid asking such questions that make Islam seem narrow-minded and extreme (not aiming this at you, OP; just something I've noticed a lot).
Saheeh Bukhari, Hadith 1
حَدَّثَنَا الْحُمَيْدِيُّ عَبْدُ اللَّهِ بْنُ الزُّبَيْرِ، قَالَ حَدَّثَنَا سُفْيَانُ، قَالَ حَدَّثَنَا يَحْيَى بْنُ سَعِيدٍ الأَنْصَارِيُّ، قَالَ أَخْبَرَنِي مُحَمَّدُ بْنُ إِبْرَاهِيمَ التَّيْمِيُّ، أَنَّهُ سَمِعَ عَلْقَمَةَ بْنَ وَقَّاصٍ اللَّيْثِيَّ، يَقُولُ سَمِعْتُ عُمَرَ بْنَ الْخَطَّابِ ـ رضى الله عنه ـ عَلَى الْمِنْبَرِ قَالَ سَمِعْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ " إِنَّمَا الأَعْمَالُ بِالنِّيَّاتِ، وَإِنَّمَا لِكُلِّ امْرِئٍ مَا نَوَى، فَمَنْ كَانَتْ هِجْرَتُهُ إِلَى دُنْيَا يُصِيبُهَا أَوْ إِلَى امْرَأَةٍ يَنْكِحُهَا فَهِجْرَتُهُ إِلَى مَا هَاجَرَ إِلَيْهِ "
Narrated 'Umar bin Al-Khattab (may Allah be pleased with him):
I heard Allah's Apostle (Peace be upon him) saying, "The reward of deeds depends upon the intentions and every person will get the reward according to what he has intended. So whoever emigrated for worldly benefits or for a woman to marry, his emigration was for what he emigrated for."
Given that the intention is to write a story where a certain character is abusive and you want to demonstrate their abusiveness by certain abusive words, then this is not haram.
It would be haram if say, you were being deceitful, and pretending to write a work of fiction, whereas in fact, you are slandering someone real by portraying him (or her) with a slightly altered name in fiction or by incidents in their lives. This has been known to happen.
And Allah knows best.