He was born on August 12, 1975, in the village of Hulbakhor, Tashkent region. When Zevri was 18 years old, his family returned to Crimea after the deportation.

Soon after, Zevri Abseitov was drafted into military service.

After military service, Zevri Abseitov entered the Simferopol Medical University, the faculty of Dentistry. In his free time, he worked to help his elderly parents.

After receiving his medical education, Zevri lived in Bakhchysarai and worked as a dentist.

On May 12, 2016, during raids in Bakhchysarai, Russian security forces detained four Crimean Tatars on suspicion of involvement in Hizb ut-Tahrir. Zevri Abseitov was accused of "participation in the activities of a terrorist organization" (Art. 205.5, part 2 of the RF Criminal Code) and "preparation for the violent seizure of power by an organized group by prior agreement" (Art. 35, part 2, Art. 30, part 1, and Art. 278 of the RF Criminal Code).

Abseitov and other defendants of the case were held in Simferopol SIZO for 2 years. In May 2018, all four were transferred to SIZO in Rostov-on-Don.

On December 24, 2018, the North Caucasus District Military Court in Rostov-on-Don announced verdict: Zevri was sentenced to 9 years in a strict regime colony. After the defense filed an appeal, on July 11, 2019, the Supreme Court of the Russian Federation reduced Abseitov's sentence by three months - to 8 years and 9 months.

On the night of September 1-2, 2019, Abseitov was transferred to IK-1 in the village of Kochubeyevskoye, Stavropol Krai. Immediately upon arrival, he was placed in a punishment cell for 3 weeks as a person convicted under "particularly serious article". His lawyer, Rustem Kamiliev, said that Abseitov's stay in SHIZO was illegal, as a prisoner can be placed there only in case of violations of the rules of the Federal Penitentiary Service.

On December 11, 2019, the Ukrainian Parliament Commissioner for Human Rights Liudmyla Denisova reported: "Zevri Abseitov has problems with his teeth and kidneys, as well as II-degree hypertension, which can cause a stroke unless he receives constant medical care." According to Denisova, medical staff of the colony do not provide proper medical care to Abseitov, thus violating international standards for the detention of persons deprived of their liberty.