Mathematicians dying during the war, whether in military action, detention, taking their own life or due to other factors has certainly interrupted mathematical research. However, this is only the most dramatic and visible manifestations of war's effect on the mathematical community --- there are many others. There is a well-researched book that deals with all aspects of mathematical life in Nazi Germany, both before and during WWII:
Sanford L. Segal, Mathematicians under the Nazis, Princenton University Press, 2003 (ISBN 0-691-00451-X)
Specifically on the question of Teichmüller's repugnant actions before the war, I would like to recommend
M.R. Chowdhury, Landau and Teichmüller, Mathematical Intelligencer, vol. 17, no. 2, 1995
The author concludes that
Teichmüller was instrumental in perpetrating a heinous crime, the Landau boycott, which destroyed not only a truly great man and mathematician but also a great mathematical center.
Although this article focusses on Landau, of course he was not the only Göttingen professor affected by Nazi doctrine of Aryan science, which through the infamous Berufsbeamtengesetz of 1933 eliminated other illustrious scientists, including Max Born, James Franck, Edward Teller, Eugine Wigner, Emmy Noether and Richard Courant.
If you are willing to explore the thesis that war is harmful to mathematical community, both World War I and World War II provide a lot of evidence. For example, French intellectual elite was decimated by the Great War and the country lost a whole generation of mathematicians. Several of Michèle Audin's books deal with these subjects.
Michèle Audin, Fatou, Julia, Montel: The Great Prize of Mathematical Sciences of 1918, and beyond. Springer, 2011 (ISBN 978-3-642-17854-2)
Michèle Audin, Jacques Feldbau, Topologe: Das Schicksal eines jüdischen Mathematikers (1914 - 1945). Springer, 2012 (ISBN 978-3-642-25803-9)