He was born on April 17, 1874 in San Francisco, California to Louise Antoinette Bryant Mackay and John William Mackay. His father was a silver miner and telegraph mogul who had been born in Dublin and emigrated to America with his parents. After arriving in America, his father died soon after, and John sold newspapers and got a shipyard job to support his mother and sister. Eventually, he went west, and with three partners, formed a mining corporation and discovered the "Big Bonanza" in Virginia City, Nevada, which became the largest single deposit of gold and silver ever found. More than $100 million dollars worth of gold was extracted from that mine before it was exhausted in 1898, making all of them unimaginably wealthy. His father then married his mother and adopted her daughter by an earlier marriage. They lived between Paris and New York, where they brought up this daughter and their two sons, John and Clarence.
Around 1897, Mackay met Katherine Alexander Duer, who was a beautiful debutante from an old, high society, New York family that he met on a steamship crossing between New York and England. She was a direct descendant of Lady Kitty Duer, daughter of Lord Stirling. They fell in love and were married on May 17, 1898. Harbor Hill in Roslyn, Long Island, the site of their future estate with the striking view of Hempstead Harbor, was Katherine's and Clarie's wedding present from the senior Mackays. Katherine oversaw much of the design and building of their mansion at Harbor Hill which was designed by Stanford White of McKim, Mead, and White and was the largest home White ever designed. Katherine was a suffragette and a champion of women's rights and became the first woman member of the Roslyn school board in 1905. Together, Clarence and Katherine were the parents of three children:
Katherine Mackay, who married Kenneth O'Brien in 1922. They divorced and she remarried to Robert Ziemer Hawkins in 1938.
Ellin Mackay, who fell in love with the popular composer Irving Berlin, to the fury of her father; Berlin was a Russian immigrant, an Orthodox Jewish widower fifteen years older than she. When Ellin insisted on marrying Berlin in 1926, Clarence disinherited her. However, Berlin was already wealthy at this stage, the most popular songwriter of his time.
John William Mackay, who married Josephine Gwendolyn Rose in 1929.
In 1910, Katherine left Clarence and her three children to run away with Dr. Joseph Blake, the doctor who had cured Clarence's throat cancer. Blake then cured her eye cancer, and he in turn ran away with her nurse. The marriage officially ended in divorce in Paris in 1914. Katherine returned to New York in 1930, the same year she died from cancer. Because of religious convictions, he was a traditional Irish-American Catholic, Mackay would not remarry as long as his first wife, Katherine, lived. Therefore, Clarence and Anna Case waited until after Katherine's death in 1930, and were subsequently married in 1931 at St. Mary's Roman Catholic Church in Roslyn, New York. His wedding gift to Anna was a platinum-set emerald and diamond necklace. The emerald was mined in Colombia and the necklace designed by Cartier. Anna was a lyric soprano who sang with the Metropolitan Opera and as a concert soloist. "Her life changed dramatically following an engagement to sing at a private musicale given in the home of Clarence H. Mackay. Taken with her beauty, he sent a carload of flowers to her at her next Carnegie Hall recital, enclosing a small diamond band with an enamel bluebird in the center." He died of cancer on November 12, 1938. His funeral was at St. Patrick's Cathedral where the New York Philharmonic played. He was buried at Green-Wood Cemetery.