Background-free inelastic scattering spectra have been obtained for five Sm isotopes with [Formula Presented] particles at forward angles (including [Formula Presented]) to investigate the effect of deformation on the compressional-mode giant resonances. The strength distributions for the [Formula Presented] isoscalar giant resonances have been extracted via a multipole decomposition analysis using angular distributions calculated in the framework of the density-dependent single-folding model. We observed a splitting of the giant monopole resonance because of its mixing with the giant quadrupole resonance. For the isoscalar giant dipole resonance, the observed effects of deformation are different for the low- and high-excitation-energy components. Evidence has been obtained for the theoretically predicted mixing between the isoscalar giant dipole resonance and the high energy octupole resonance.