This paper presents a study of the production of \(WW\) or \(WZ\) boson pairs, with one \(W\) boson decaying to \(e\nu\) or \(\mu\nu\) and one \(W\) or \(Z\) boson decaying hadronically. The analysis uses 20.2 fb\(^{-1}\) of \(\sqrt{s}=8\) TeV \(pp\) collision data, collected by the ATLAS detector at the Large Hadron Collider. Cross-sections for \(WW/WZ\) production are measured in high-\(p_{T}\) fiducial regions defined close to the experimental event selection. The cross-section is measured for the case where the hadronically decaying boson is reconstructed as two resolved small-radius jets, and the case where it is reconstructed as a single large-radius jet. The transverse momentum distribution of the hadronically decaying boson is used to search for new physics. Observations are consistent with the Standard Model predictions, and \(95\%\) confidence intervals are calculated for parameters describing anomalous triple gauge-boson couplings.