Aluminum scandium nitride alloy (Al1-xScxN) is regarded as a promising material for high-performance acoustic devices used in wireless communication systems. Phonon scattering and heat conduction processes govern the energy dissipation in acoustic resonators, ultimately determining their performance quality. This work reports, for the first time, on phonon scattering processes and thermal conductivity in Al1-xScxN alloys with the Sc content (x) up to 0.26. The thermal conductivity measured presents a descending trend with increasing x. Temperature-dependent measurements show an increase in thermal conductivity as the temperature increases at temperatures below 200K, followed by a plateau at higher temperatures (T> 200K). Application of a virtual crystal phonon conduction model allows us to elucidate the effects of boundary and alloy scattering on the observed thermal conductivity behaviors. We further demonstrate that the alloy scattering is caused mainly by strain-field difference, and less by the atomic mass difference between ScN and AlN, which is in contrast to the well-studied Al1-xGaxN and SixGe1-x alloy systems where atomic mass difference dominates the alloy scattering. This work studies and provides the quantitative knowledge for phonon scattering and the thermal conductivity in Al1-xScxN, paving the way for future investigation of materials and design of acoustic devices.