Clinical diagnoses of bone health and fracture risk typically rely on measurements of bone density or structure, but the strength of a bone is also dependent on its chemical composition. Raman spectroscopy has been used extensively in ex vivo studies to measure the chemical composition of bone. Recently, spatially offset Raman spectroscopy (SORS) has been utilized to measure bone transcutaneously. Although the results are promising, further advancements are necessary to make noninvasive, in vivo measurements of bone with SORS that are of sufficient quality to generate accurate predictions of fracture risk. In order to separate the signals from bone and soft tissue that contribute to a transcutaneous measurement, we developed an overconstrained extraction algorithm that is based on fitting with spectral libraries. This approach allows for accurate spectral unmixing despite the fact that similar chemical components (e.g., type I collagen) are present in both bone and soft tissue. The algorithm was utilized to transcutaneously detect biochemical differences in the tibiae of wild-type mice between 1 and 7 months of age and between the tibiae of wild-type mice and a mouse model of osteogenesis imperfecta. These results represent the first diagnostically sensitive, transcutaneous measurements of bone using SORS.