The Çadır Köşk (Tent Kiosk), one of two pavilions in the park, has this inscription.

"Mithat Paşa, Sultan Abdülazizi öldürttügü iddia ve Ithamiyle Sultan Abdülhamit tarafından, muhakeme edilmek üzre, 22 mayis 1881 Pazar günü bu köşke getirilmiş ve ihtilattan memnü olarak hapsedilmiştir. 22 temmüz 1881 Perşembe günü de buradan alınarak izzettin vapuriyle taife sürülmüş ve orada şehit edilmiştir."

I could not make head or tail from this, but then found on the Wikipedia:

Ahmed Şefik Midhat Pasha (1822 – 26 April 1883) was one of the leading Ottoman statesmen during the late Tanzimat era. He is most famous for leading the Ottoman constitutional movement of 1876, but was also a leading figure of Ottoman reform in the educational and provincial administrations. He was part of a governing elite which understood clearly the profound crisis in which the empire versed, and considered reform to be a dire need.
He was described by Caroline Finkel as "a true representative of Tanzimat optimism, who believed that separatist tendencies could be best countered by demonstrating the benefits of good government." For the British, his reforming zeal was an aberration, based on individual strength of personality. They believed Midhat Pasha could not succeed, given the inherently inefficient and corrupt nature of the Ottoman state, and the oppressed and fractured nature of its society.
Midhat Pasha was also a prominent advocate of the abolition of slavery in the Ottoman Empire; he pressured Sultan Abdul Hamid II into emancipating the slaves of the palace, and he himself freed any slave he received as a gift from others. His second wife, with whom he had three children, was a Circassian slave he had purchased and then freed.
The Medhat Pasha Souq in Damascus still bears his name.

And:

He served briefly in Izmir as governor of the vilayet of Aydin, but on 17 May 1881, after only a few months on that post, he was arrested. Ahmed Cevdet Pasha, the justice minister, brought him to Istanbul, where he was charged with the murder of Sultan Abdulaziz. The interrogation and court proceedings took place at Yildiz. Most historians believe these to be trumped-up accusations. Confessions were extracted from some suspects through the use of torture. The use of forged evidence and paid witnesses led to his conviction, and he was sentenced to death.
British pressure impeded his execution, so he was imprisoned in the fortress of Taif, in Hejaz. It was reported that, soon after his arrival, the Emir of Mecca received a message from Constantinople demanding the death of Midhat from "an accident". The incumbent Emir Abdul Muttalib was a close friend of Midhat however, and no action was taken by him. As a result, Osman Pasha, governor of Hejaz, surrounded the Emir's summer residence in Taif and imprisoned him.
After that, Midhat Pasha's fate was sealed. He was assassinated in his cell on 26 April 1883.