SrYb₂O₄  is a geometrically frustrated rare-earth magnet, which presents a variety of interrelated magnetic phenomena. The magnetic Yb³⁺ ions (J = 7/2) form potentially frustrated “zigzag” chains along the c axis, arranged in a honeycomb fashion in the ab plane. Heat capacity reveals a magnetic phase transition at T_N = 0.9 K. The magnetic structure was solved by polarized neutron diffraction and found to be noncollinear with a reduction of the ordered spin moment from the full ionic moment. The low-energy excitations, which were measured by inelastic neutron scattering reveal diffuse scattering both above and below T_N. Heat capacity and magnetocaloric effect were performed to map out the magnetic phase diagram as a function of magnetic field and temperature and show a complicated series of states. Altogether, the results suggest that the magnetic interactions in SrYb₂O₄  compete with each other and with the single-ion anisotropy to produce a highly degenerate ground state manifold that suppresses the magnetic order, broadens the excitations and gives rise to a complex phase diagram.