The Strong Winds Ministry Church in Las Tunas, eastern Cuba, is affiliated with the Apostolic Protestant Movement and is the fourth in Cuba - and the second in Las Tunas - to be demolished by the government since the start of the year.
Hundreds of government officials surrounded the church and reportedly used heavy machinery to break up the floor, pews and equipment.
Reverend Travieso claims he was "treated badly" by the head of the State Security Provincial unit and was presented with a pre-arrest warrant which includes a seven-year prison sentence if anyone in the congregation makes public complaints about the destruction of their church.
Despite these threats, Revd Travieso said "All of these violations continue in my country, without any attention, so we share the news of this great injustice with the international community."
By Dan Golding