Nasmyth joined Ben Hall's lab in Seattle as a postdoctoral researcher where he developed ways of cloning genes by complementation in yeast and, in collaboration with Steve Reed, cloned the CDC28 gene from the budding yeast Saccharomyces cerevisiae. As a group leader in Cambridge Nasmyth became interested in the phenomenon of mating-type switching in yeast. Together with Kelly Tatchell he cloned the S. cerevisiae mating-type locus and found, surprisingly, that 'silent' copies of the mating-type genes including their promoters are maintained in the yeast chromosome. This represented the first case where the position of a gene in the chromosome had demonstrable biological significance, and prompted Nasmyth to abandon work on the cell cycle for a time and concentrate instead on studying gene silencing. He was one of the first to demonstrate that gene expression can be regulated through specific control elements which are distant from the start of transcription. Max Birnstiel invited Nasmyth to join him at the then newly founded Research Institute of Molecular Pathology in Vienna, Austria, where he was director. Nasmyth became one of the first three senior group leaders that Birnstiel recruited in 1986. At the IMP, Nasmyth changed his focus from gene silencing back to cell cycle control. In the mid-1990s Nasmyth co-discovered the APC/C and showed that its activity induces chromosome segregation. Using temperature-sensitive mutants of the APC/C he found several genes which are required for sister chromatid cohesion which we now know encode subunits of the cohesin complex. Nasmyth has since shown that cohesin forms a ring, that sister chromatids are held together within this ring and that they are released by cleavage of cohesin by separase. Following Max Birnstiel's retirement, Nasmyth became scientific director of the IMP in 1997. In 2006, Nasmyth left the IMP to become head of the Department of Biochemistry of the University of Oxford, a post he held until 2011. Nasmyth continues to head a research group at this department. He is a member of the Advisory Council for the Campaign for Science and Engineering. His research has been funded by the Medical Research Council, the Wellcome Trust, and Cancer Research UK. He plans to retire from research in 2022.
Nasmyth married Anna Dowson, daughter of Sir Philip Dowson, in 1982 and has two daughters. His brother is furniture designer Luke Hughes. He enjoys skiing and climbing, a hobby to which he attributes his theory of how cohesin works. He also co-owns a vinyard in the south of France. Nasmyth held a large number of shares in his fathers billion dollar company Argus Media until its purchase by General Atlantic in 2016. In 2014 he was appointed director of Badger Lane Management company. During his time in Vienna, Nasmyth became Austrian citizen.