Crowley received his early education in his home town of Cork. He attended the University of Glasgow and the Royal University of Edinburgh in Scotland where he obtained a medical degree. He practiced medicine for 33 years.
He was elected as a Sinn Féin MP for the Mayo North constituency at the 1918 general election. In January 1919, Sinn Féin MPs refused to recognise the Parliament of the United Kingdom and instead assembled at the Mansion House in Dublin as a revolutionary parliament called Dáil Éireann.
He was elected unopposed as a Sinn Féin Teachta Dála (TD) for the Mayo North and West constituency at the 1921 elections. He opposed the Anglo-Irish Treaty and voted against it.
He was re-elected unopposed for the same constituency at the 1922 general election, this time as an anti-Treaty Sinn Féin TD, and he did not take his seat in the Dáil. He was elected as a Republican TD for Mayo North constituency at the 1923 general election and once again he did not take his seat. He did not contest the June 1927 general election.
Dr. Crowley was a devout Catholic. He married Julia Catherine Larkin in 1903. They had five children, four daughters and one son, Finbar, who passed away at the age of 3.
Dr. Crowley died in 1934 at the age of 64. His burial mass was at St. Brigid's CHurch in Ballycastle and presided over by the Most Rev. Dr. Naughton, Bishop of Killala. In attendance at his funeral were 1000 Old IRA members, Mr. P.J. Rutledge, the Minister for Justice, and many other T.D.s. The Minister for Justice, Mr. P.J. Rutledge was also present, as were many T.D.’s. He was buried in Doonfeeny Cemetery with his son Finbar.
A monument for Dr. Crowley was erected on Killala Road in Ballycastle. The inscription on the monument reads:
After Dr. Crowley's death in 1934, a song was written in his tribute:
Oh mourn you true Irishmen An Irish Patriot brave A fearless champion of the cause Today rests in his grave.
Brave Dr. Crowley is no more A true son of Inisfail And many hearts in dear Mayo His loss will long bewail
A gloom o’erspread the district When Dr. Crowley died He loved and much respected was Within the country wide.
From Achills cliffs to Clew Bay shore From the May to Lackan Strand On every side the cry is heard, Brave Crowley is no more.
A noble son of Rebel Cork Where he first saw the light And trod the path of early youth Of truth and virtue bright.
When Ireland’s trumpet call rang out By hill and town and sea, He marched proud with strength held high The banner of Sinn Fein
In Twenty and in Twenty-one Sad but glorious years When Ireland's brooins call rang out He led the volunteers.
A pure forth patriot kind and true He loved his country well In Potter’s cease he long endured The dreary prison cell.
So dear to all who knew him well His loved and honoured comrades His deeds will be remembered round Till Ireland’s one again.
He learned his native language Brilliantly spoke the Gaelic tongue, He read and wrote it fluently The respect of all was won.
Our Parliament was stifled A leader they did need He joined with other members To form the first Dail freed.
In the medical profession His equals they were few O mind, Mayo peasantry He laboured hard for you.
By his friends in Ballycastle He will long remembered be And by his boyhood comrades Down by the River Lee.
That place he left when but a boy So many years ago He made his home here by the sea Where the glen’s great waters flow.
Within Dunfinn Churchyard His body laid to rest Above his tomb are evergreens And yonder yew tree waves.
We pray his soul in heaven rests Among God’s holy angels blest.