We present the first complete 55-671 um spectral scan of a low-mass Class 0 protostar (Serpens SMM1) taken with the PACS and SPIRE spectrometers on board Herschel. More than 145 lines have been detected, most of them rotationally excited lines of 12CO (full ladder from J=4-3 to 42-41), H2O, OH, 13CO, HCN and HCO+ . Bright [OI]63,145um and weaker [CII]158 and [CI]370,609um lines are also detected. Mid-IR spectra retrieved from the Spitzer archive are also first discussed here, they show clear detections of [NeII], [FeII], [SiII] and [SI] fine structure lines as well as weaker H2 S(1) and S(2) pure rotational lines. The observed line luminosity is dominated by CO (~54%), H2O (~22%), [OI] (~12%) and OH (~9%) emission. A non-LTE radiative transfer model allowed us to quantify the contribution of the 3 different temperature components suggested by the 12CO rotational ladder (Tk(hot)~800 K, Tk(warm)~375 K and Tk(cool)~150 K). Gas densities n(H2)~5x10^6 cm^-3 are needed to reproduce the observed far-IR lines arising from shocks in the inner protostellar envelope for which we derive upper limit abundances of x(CO)~10^-4, x(H2O)~0.2x10^-5 and x(OH)~10^-6. The lower energy submm 12CO and H2O lines show more extended emission that we associate with the cool entrained outflow gas. Fast dissociative J-shocks (v_s > 60 km s^-1) as well as lower velocity non-dissociative shocks (v_s