Dissociative recombination (DR) of the water cluster ions H(+)(H(2)O)(3) and D(+)(D(2)O)(3) with electrons has been studied at the heavy-ion storage ring CRYRING (Manne Siegbahn Laboratory, Stockholm University). For the first time, absolute DR cross sections have been measured for H(+)(H(2)O)(3) in the energy range of 0.001-0.8 eV, and relative cross sections have been measured for D(+)(D(2)O)(3) in the energy range of 0.001-1.0 eV. The DR cross sections for H(+)(H(2)O)(3) are larger than previously observed for H(+)(H(2)O)(n) (n=1,2), which is in agreement with the previously observed trend indicating that the DR rate coefficient increases with size of the water cluster ion. Branching ratios have been determined for the dominating product channels. Dissociative recombination of H(+)(H(2)O)(3) mainly results in the formation of 3H(2)O+H (probability of 0.95+/-0.05) and with a possible minor channel resulting in 2H(2)O+OH+H(2) (0.05+/-0.05). The dominating channels for DR of D(+)(D(2)O)(3) are 3D(2)O+D (0.88+/-0.03) and 2D(2)O+OD+D(2) (0.09+/-0.02). The branching ratios are comparable to earlier DR results for H(+)(H(2)O)(2) and D(+)(D(2)O)(2), which gave 2X(2)O+X (X=H,D) with a probability of over 0.9.