This Letter presents a search for new physics manifested as anomalous triple gauge boson couplings in WW and WZ diboson production in proton-proton collisions. The search is performed using events containing a W boson that decays leptonically and a W or Z boson whose decay products are merged into a single reconstructed jet. The data, collected at $ \sqrt{s} = $ 8 TeV with the CMS detector at the LHC, correspond to an integrated luminosity of 19 fb$^{-1}$. No evidence for anomalous triple gauge couplings is found and the following 95% confidence level limits are set on their values: $λ$ ($ [-0.011,0.011]$), $\Delta{\kappa_\gamma}$ ($ [-0.044,0.063]$), and $\Delta{g_1^{\mathrm{ Z }}}$ ($ [-0.0087,0.024]$). These limits are also translated into their effective field theory equivalents: $c_{\mathrm{ WWW }}/Λ^2$ ($ [-2.7,2.7]$ TeV$^{-2}$), $c_\mathrm{B}/Λ^2$ ($ [-14,17]$ TeV$^{-2}$), and $c_{\mathrm{ W }}/Λ^2$ ($ [-2.0,5.7]$ TeV$^{-2}$).