No, Turkmenistan Airlines has no scheduled flights out of Dublin. However, Turkmenistan Airlines does fly out of Frankfurt am Main. There are also other airline options to choose from if you still want to book a flight from Dublin. Air Canada, for example, is an airline that flies out of Dublin on a regular basis.
Dashoguz is the most popular airport that Turkmenistan Airlines serves, followed by Ashgabat and Turkmenabad.