In the audio statement, the group's new spokesman, Abu Hassan al-Muhajer, said America had “drowned” and was ruled by someone who “does not know what Syria or Iraq or Islam is”.
It is Isis' first official comment on Mr Trump since the Republican's inauguration in January.
“America you have drowned and there is no saviour, and you have become prey for the soldiers of the caliphate in every part of the earth, you are bankrupt and the signs of your demise are evident to every eye,' al-Muhajer said
“There is no more evidence than (that) you being run by an idiot who does not know what Syria or Iraq or Islam is.
“Die of spite America, die of spite, a nation where both young and old are racing to die in the name of God will not be defeated.”
The comments were made during a 37-minute recording released on the messaging website Telegram.
During the address, al-Muhajer also praised recent terrorist attacks in Europe and called for Isis followers to carry out further attacks in the US, Russia and EU states in order to relieve pressure on the group in Iraq and Syria.
He said the current situation, in which Isis is engaged in heavy fighting with Iraqi troops in Mosul, the group’s last stronghold in Iraq, marked “the greatest period in our jihad…and the most dangerous turning point in our jihad”.
The spokesman also claimed Isis would never be driven from the Middle East and would continue to maintain strongholds in Syria, Iraq and Yemen.
During last year’s presidential election campaign, the group released a document calling Mr Trump “impulsive and unpredictable”.