A time-dependent study of the oxidative shortening of single-walled carbon nanotubes by concentrated nitric and sulfuric acids has been carried out. A polishing step using sulfuric acid and hydrogen peroxide was used to remove the amorphous carbon produced by the defect-creating oxidation treatment. An empirical relationship L = 691e(-1.26t) + 83.2 between oxidation time (t/hours) and nanotube length (L/nanometers) was determined from analysis of the oxidized tubes using transmission electron microscopy and Raman spectroscopy. The experimental results are discussed in comparison to a basic theoretical model for cutting of nanotubes. The results are not consistent with a time-linear ("fuse burning") mechanism as reported previously in the literature, but support a mechanism of shortening whereby defects are created at random points along the length of the tubes, followed by cleavage of the tube.