In recent years, the rapid growth of traffic has become a serious problem of mobile network operators. For effectively mitigating this traffic explosion problem, there have been many efforts to research on offloading the traffic from cellular links to direct communications among users. In this paper, we are motivated by users' sharing activities, and hence propose the framework of Traffic Offloading assisted by Social network services (SNS) via opportunistic Sharing in mobile social networks (MSNs), TOSS, to offload SNS-based cellular traffic by user-to-user sharing. First, a subset of users who are to receive the same content was selected as initial population depending on their content spreading impacts in the online SNSs and their mobility patterns in the offline MSNs. Then users move, encounter and share the content via opportunistic local connectivity with each other, the content via opportunistic local connectivity with each other, e.g., Bluetooth, Wi-Fi Direct, Device-to-Device in LTE. Individual users have distinct access patterns, which potentially allow TOSS to exploit the user-dependent access delay between the content generation time and each user's access time for content sharing purposes. The traffic offloading and content spreading among users are analyzed by taking into account various options in linking SNS and MSN traces. Four mobility traces and online SNS trace for evaluation are analyzed. An extended evaluation over a large-scale data set are further carried out, and the effectiveness of TOSS is further proved.