We present the results of stereoscopic observations of the satellite galaxy Segue 1 with the MAGIC Telescopes, carried out between 2011 and 2013. With almost 160 hours of good-quality data, this is the deepest observational campaign on any dwarf galaxy performed so far in the very high energy range of the electromagnetic spectrum. We search this large data sample for signals of dark matter particles in the mass range between 100 GeV and 20 TeV. For this we use the full likelihood analysis method, which provides optimal sensitivity to characteristic gamma-ray spectral features, like those expected from dark matter annihilation or decay. In particular, we focus our search on gamma-rays produced from different final state Standard Model particles, annihilation with internal bremsstrahlung, monochromatic lines and box-shaped signals. Our results represent the most stringent constraints to the annihilation cross-section or decay lifetime obtained from observations of satellite galaxies, for masses above few hundred GeV. In particular, our strongest limit (95% confidence level) corresponds to a ~ 500 GeV dark matter particle annihilating into τ+τ−, and is of order langleσannvrangle simeq 1.2 × 10−24 cm3 s−1 a factor ~ 40 above the langleσannvrangle simeq thermal value.