Trcka was born on 6 July 1886 in the small town of Frydlant nad Ostravici in the present day Czech Republic. He was the seventh, and youngest, child of Tomas Trcka and Frantiska Sterbova Trcka; like many families of that time and region, the Trckas were devout Catholics.
Dominick entered the Redemptorist novitiate in Bilsko, Poland when he was only 17 years of age, although this was nothing unusual in that era. After making his first profession on 25 August 1904, he returned to Obořiště in his homeland so that he could pursue the required studies in philosophy andtheology.
On 17 July 1910 he was ordained, by Cardinal Lev Skrbenský z Hříště, to the Presbyterate within the Latin Rite branch of the Catholic Church. After spending some years engaged in the traditional Redemptorist ministry of conducting parish missions, Father Dominick was sent to serve the Greek Catholics in Halič in what is now the Banská Bystrica Region of Slovakia. Eastern Rite Catholics were often overlooked in number and importance, not only by Orthodox believers but also by Roman CatholicChristians even though both groups are in communion with the Bishop of Rome. Trcka worked tirelessly to redress the situation and one of his most significant achievements was organising the establishment, inMichalovce, of a monastery for Eastern Rite Redemptorists.
In 1935, when the Redemptorist communities of the area were re-organised Father Trcka was appointed as vice-provincial of the Byzantine Catholic Redemptorists.
With the Communist take over of Czechoslovakia, a period of religious persecution began and, in 1950, all religious communities were suppressed by the government. On the evening of 13 April (which happened to be Holy Thursday) Father Trcka was arrested along with several other Redemptorists. He was put on trial and accused of trying to obtain false papers in order to flee the country and was sentenced to 12 years in prison. During his imprisonment, Father Dominick, like many other Catholic priests and religious, endured both torture and interrogation; however, being one of the Church leaders, it seems that he was made to bear more frequent abuse. One of his confreres, who was released, wrote that they were subjected to intense light 24 hours a day.
On 23 March 1959, he died as the result of pneumonia, having been placed in solitary confinement as a punishment for singing Christmas carols. In 1969, his remains were exhumed and placed in the Redemptorist crypt in Michalovce Cemetery.
Father Dominick was declared a martyr by Pope John Paul II on 24 April 2001 and beatified by the same pope on 4 November 2001.