Abashidze was born into a renowned Muslim Ajarian family. His grandfather was one of the leaders of the briefly independent Democratic Republic of Georgia between 1918-1921 but was shot on Stalin's order in 1937. His father was sent to the Gulag for ten years but survived. Despite a difficult childhood, during the 1950s Abashidze was able to obtain degrees in history and philosophy at Batumi University and in economics at Tbilisi State University. He worked as a teacher and economist for a period before joining Georgia's regional public service. He directed several technical-service institutes before being named a regional minister in Batumi, the capital of Ajaria, where he served as Minister of Community Service. He was later appointed the national First Deputy Minister of Community Service and moved to Tblisi. This was, however, a relatively minor government post.
When Georgia regained its independence in 1991, Abashidze secured his appointment as Chairman of the Supreme Council of the Autonomous Republic of Ajaria. He was also appointed Vice-President of Georgia, a post that he retained until 1996. He built an independent power base in Ajaria by steering a course between the erratic rule of President Zviad Gamsakhurdia and the opposition. When civil war broke out between pro- and anti-Gamsakhurdia forces in the winter of 1991-92 and again in the autumn of 1993, he established his own Ajarian army. He kept both the government forces and those of Gamsakhurdia's rebels out of Ajaria, ensuring that the fighting did not spread to the republic.
However, unlike the rulers of Abkhazia and South Ossetia, he did not attempt to seek independence for Ajaria and pursued what can best be described as a policy of "armed autonomy" after the fall of Gamsakhurdia. He effectively turned Ajaria into a "free economic zone" with few restrictions on trade (and, reportedly, smuggling) but with the customs duties and revenues going to his government rather than Tblisi. His economic policies have been quite successful and have made Ajaria one of the wealthier parts of Georgia.
Abashidze has attracted some criticism for heavy-handed rule, which has often been described as feudal, but he appears to be genuinely popular among Ajarians. He established his own political party in 1992, known variously as the Union of Democratic Revival or the Union for Georgia's Rebirth. In 1998, he was elected President of Ajaria with 93% of the vote in what Russian observers regarded as a generally free and fair election (although this verdict may have been influenced by Abashidze's consistently pro-Russian policies).
He has preferred to exercise influence from a distance, rather than attempting to bid for national power, and has consistently adopted a policy of backing whoever seems to offer the best deal for maintaining his rule over Ajaria. He reached an accomodation with President Eduard Shevardnadze, who appears to have preferred to have preferred to live with a semi-independent Ajaria rather than risk another civil war. His relations with Shevardnadze grew frosty at the end of the 1990s, as he and the government traded accusations of corruption and treason.
The forced resignation of Shevardnadze in November 2003 created a political crisis between Abashidze and the new government in Tblisi. The Georgian opposition had strongly criticised Shevardnadze for failing to resolve the problem of separatism in the country, including what they saw as the lack of control which Tblisi had over Ajaria. Not surprisingly, Abashidze saw this as a threat to his position and the continued semi-independence of Ajaria, and denounced the downfall of Shevardnadze as a "coup". He declared a state of emergency in Ajaria and sought Russian support in the event of an open conflict. However, he failed to attract much support from Russia and came under intense pressure from the United States to compromise. He has declared his intention to work with the newly-elected President Mikhail Saakashvili but relations still remain tense.