Traceback has been very attractive against DDoS attacks with IP spoofing instead of traditional mitigation methods because attacks require removal near attackers, resulting in affecting legitimate traffic as little as possible. There have been some approaches dedicated to achieving effective traceback. However, existing approaches often modify protocols to apply to multi-domain scenarios, and the implemented mitigation usually lags behind traceback. Therefore, this paper proposes the Software-Defined Multi-Domain Network Tracer and Mitigator (SD-MDN-TM) to traceback and mitigate DDoS attacks with IP spoofing in multi-domain SDN scenarios. We apply systematic sampling and flow feature extraction based on the Count-Min Sketch data structure for the lightweight statistics collection of massive DDoS attack traffic. We also design the TracebackTree data structure to construct the traceback paths of attackers of distributed attack sources. The Border Switch Trigger Mechanism is proposed to overcome the drawbacks of the commonly-used packet marking in cross-domain traceback information transfer, achieving no modification of existing network protocols and independent traceback among multiple domains. Mitigation is integrated with traceback for faster removal of attacks from the network. The proposed scheme can traceback DDoS attack sources both inside and outside domains accurately and effectively by constructing traceback path. It can be implemented without modifying the existing protocols, therefore achieving direct application to the existing network architecture. Furthermore, the traceback of attack sources outside domains can maintain independence in multi-domain scenarios. Mitigation integrated with traceback can achieve less impact on legitimate traffic and faster removal of attacks from the network.