Supernova surveys can be used to study a variety of subjects such as: (i) cosmology through type Ia supernovae (SNe), (ii) star-formation rates through core-collapse SNe, and (iii) supernova properties and their connection to host galaxy characteristics. The Stockholm VIMOS Supernova Survey (SVISS) is a multi-band imaging survey aiming to detect supernovae at redshift similar to 0.5 and derive thermonuclear and core-collapse supernova rates at high redshift. In this paper we present the supernovae discovered in the survey along with light curves and a photometric classification into thermonuclear and core-collapse types. To detect the supernovae in the VLT/VIMOS multi-epoch images, we used difference imaging and a combination of automatic and manual source detection to minimise the number of spurious detections. Photometry for the found variable sources was obtained and careful simulations were made to estimate correct errors. The light curves were typed using a Bayesian probability method and Monte Carlo simulations were used to study misclassification. We detected 16 supernovae, nine of which had a core-collapse origin and seven had a thermonuclear origin. The estimated misclassification errors are quite small, in the order of 5%, but vary with both redshift and type. The mean redshift of the supernovae is 0.58. Additionally, we found a variable source with a very extended light curve that could possibly be a pair instability supernova.