Grogan initially trained in Cork under the local painter John Butts, with Dutch painters such as Hobbema and Heemskerck as his key influences. He had begun life as an apprentice to his father, a turner and block maker, but had a love for the arts and taught himself to draw. At his fathers request, he enlisted in the British army and served in America during the War of Independence. Little, if any, is known of the paintings he produced in the New World. Grogan went on to produce numerous oil and watercolour paintings depicting landscapes and genre scenes of his native Cork. His son also became a painter, achieving some success.
The View of Cork in the collection of the city's Crawford Art Gallery, previously believed to be by Grogan, is now attributed to his teacher, John Butts.