Rothmuller earned both his bachelor's and master's degrees at the Indiana University School of Music, where he was a student of Fritz Magg. He also studied with János Starker and participated in the USC Piatigorsky Master Class. Rothmuller joined the Los Angeles Philharmonic during the 1970/71 season and was appointed to the position of Associate Principal Cellist in 1975. He has won critical praise for his many solo appearances with the Philharmonic, both in the Dorothy Chandler Pavilion and at the Hollywood Bowl, under Music Directors Esa-Pekka Salonen, André Previn, Carlo Maria Giulini, and Zubin Mehta, and composer Witold Lutoslawski. Under the latter's baton he gave the first West Coast performances of the renowned Polish composer's Cello Concerto. During the Philharmonic's 1995 celebration of the Hindemith Centenary, Rothmuller performed Hindemith's Cello Concerto under the direction of Franz Welser-Möst. In the first Green Umbrella concert of the 1998/99 season, he gave the West Coast premiere of the Cello Concerto of HK Gruber in a performance conducted by the composer. He has also been featured in special Philharmonic concerts at UCLA, in various southern California communities, and in Philharmonic chamber and new music programs. He retired in September of 2012.
An avid chamber musician, Rothmuller has performed with various ensembles in Europe, Los Angeles, New York, and Washington, D.C.; on the Bronfman Chamber Music Series at Sun Valley, Idaho; at the White Mountain Festival in New Hampshire; and festivals in Round Top, Texas, and Rockport, Massachusetts. He is an original member of the Los Angeles Philharmonic Chamber Music Society and the Philharmonic New Music Group, and also a member of the ensembles An die Musik and the Jordan Piano Trio.
Daniel Rothmuller has participated in several music festivals, including the Aspen Music Festival, at which he was both on the faculty and was Principal Cellist of the Aspen Festival Orchestra; the Colorado Music Festival at Boulder, where he also served as Principal Cellist; and the Sun Valley Summer Symphony at Sun Valley, Idaho.