He graduated from Harvard College in 1915, and then from Harvard medical school in 1920. He worked by the Boston City Hospital and in the New York Neurological Institute at Columbia University. He was promoted to director after his works with phenytoin.
At his time there were quotas for Jewish physicians. He opposed the existence of the quotas. He was forced to resign from Columbia in 1947, maybe because of this. However, other sources mention a "personal tragedy" Putnam went through at that time (presumably the death of his daughter, Lucy Washburn Putnam on September 24, 1947), after which he resigned from Columbia and abandoned all scientific activities.
He studied multiple sclerosis together with Alexandra Adler. He was one of the first persons to propose, as early as the 1930s, a vascular cause for multiple sclerosis, resurrecting the previous works from Eduard von Rindfleisch. The idea remained obscure until the syndrome of chronic cerebrospinal venous insufficiency (CCSVI) was associated with the multiple sclerosis in 2008.
- Lewis P. Rowland, The Legacy of Tracy J. Putnam and H. Houston Merritt: Modern Neurology in the United States, Arch Neurol. 2009; 66(3):415.
- The Society of Neurological Surgeons, Decease Member, Tracy J. Putnam, MD 
- Lewis P. Rowland, The Legacy of Tracy J. Putnam and H. Houston Merritt: Modern Neurology in the United States, N Engl J Med 2009; 360:941–942, February 26, 2009
- Barron H. Lerner, In a Time of Quotas, a Quiet Pose in Defiance
- L. P. Rowland, Epilepsia vol 23(Suppl.I):SI-S4, 1982
- Putnam T and Adler A: Vascular architecture of the lesions of multiple sclerosis. Arch Neurol Psychiat 1937; 38:1
- Putnam T: Evidences of vascular occlusion in multiple sclerosis and encephalomyelitis. Arch Neurol Psychiatry 1937; 37(6):1298–1321.