Mutations in spastin are the most common cause of hereditary spastic paraplegia (HSP) but the mechanisms by which mutant spastin induces disease are not clear. Spastin functions to regulate microtubule organisation, and because of the essential role of microtubules in axonal transport, this has led to the suggestion that defects in axonal transport may underlie at least part of the disease process in HSP. However, as yet there is no direct evidence to support this notion. Here we analysed axonal transport in a novel mouse model of spastin‐induced HSP that involves a pathogenic splice site mutation, which leads to a loss of spastin protein. A mutation located within the same splice site has been previously described in HSP. Spastin mice develop gait abnormalities that correlate with phenotypes seen in HSP patients and also axonal swellings containing cytoskeletal proteins, mitochondria and the amyloid precursor protein (APP). Pathological analyses of human HSP cases caused by spastin mutations revealed the presence of similar axonal swellings. To determine whether mutant spastin influenced axonal transport we quantified transport of two cargoes, mitochondria and APP‐containing membrane bound organelles, in neurons from mutant spastin and control mice, using time‐lapse microscopy. We found that mutant spastin perturbs anterograde transport of both cargoes. In neurons with axonal swellings we found that the mitochondrial axonal transport defects were exacerbated; distal to axonal swellings both anterograde and retrograde transport were severely reduced. These results strongly support a direct role for defective axonal transport in the pathogenesis of HSP because of spastin mutation.