The demise of a wicked person is cause for joy and a source of relief for the Muslim Ummah

Narrated Abū Qatādah raḍhiyallāhu ’anhu:

“We were sitting with the Messenger of Allāh ﷺ when a funeral procession passed by.

The Messenger of Allāh said:
((مُسْتَرِيحٌ وَمُسْتَرَاحٌ مِنْهُ))
“One is relieved and another others are relieved from.”

When asked what he meant by these words he ﷺ replied:
((الْعَبْدُ الْمُؤْمِنُ يَسْتَرِيحُ مِنْ نَصَبِ الدُّنْيَا وَأَذَاهَا إِلَى رَحْمَةِ اللَّهِ وَالْعَبْدُ الْفَاجِرُ يستريح مِنْهُ الْعباد والبلاد وَالشَّجر وَالدَّوَاب))
“A believer is relieved (by death) from the troubles and hardships of the world and leaves for the Mercy of Allāh, while (the death of) a wicked person relieves the people, the land, the trees, (and) the animals from him.”

[Reported by Bukhāri and Muslim]

____

It was said to Imām Aḥmad ibn Ḥanbal, may Allāh have mercy on him: “If a man rejoices at what befalls the companions of Ibn Abi Du’ād, is there any sin upon him for that?” He, may Allāh have mercy on him, replied: 
ومَن لا يَفرَحُ بهذا؟!
“And who would not rejoice at that!?”
السنة للخلال ( ١٧٦٩)

_

Imam Ibn Kathīr, may Allāh have mercy on him, said in the events of the year 568 AH regarding Al-Ḥasan ibn Ṣāfi Yazdin At-Turki:

«كان من أكابر أمراء بغداد المُتحكِّمين في الدُّولة، ولكنه كان رافضيًّا خبيتًا مُتعصّبًا للرَّوافض. وكانوا في خفارته وجاهه حتى أراح الله المُسلِمينَ منه في هذه السنة في ذِي الحِجَّةِ منها، ودفن بداره، ثم نُقِل إلى مقابر قريش: فلله الحمد والمنة، وحين مات فرح أهل السُّنَّة بموته فرحا شديدًا، وأظهروا الشكر لله: فلا تَجِدُ أحدًا منهم إِلّا يَحْمَدُ الله»

“He was one of the great commanders of Baghdad who held significant influence over the state, but he was a vile Rāfḍhi, deeply prejudiced in favour of the Rawāfiḍh. They were under his protection and influence until Allāh relieved the Muslims from him in this year, in the month of Dhul Ḥijjah. He was buried in his home, then later transferred to the Cemeteries of Quraysh. All praise and thanks be to Allāh. When he died, the people of Ahlus-Sunnah rejoiced greatly at his death, and they openly expressed their gratitude to Allāh. You would not find a single one of them except that he praised Allāh.”
البداية والنهاية ( ۱۲/ ۲۷۲)
____

The permissibility of performing the prostration of gratitude upon the death of tyrants and leaders of disbelief

سجد أبو بكر رضي الله عنه شكرا حين جاءه خبر قتل مسيلمة الكذاب. وسجد علي رضي الله عنه حين رأى ذا الثدية بين قتلى الخوارج.

Abū Bakr (Aṣ-Ṣiddeeq) may Allāh be pleased with him, prostrated in gratitude when he received news of the death of Musaylimah the Liar. Similarly, ’Ali, may Allāh be pleased with him, prostrated when he saw Dhu Ath-Thadyah among the dead of the Khawarij. 
مصنف ابن أبى شيبة ( ٣٦٦ – ٢/٣٦٨)