Autism Spectrum Disorder (ASD) impacts 1 in 68 children in the U.S. with tremendous consequent cost in terms of care and treatment. Evidence suggests that early intervention is critical for optimal treatment results. Robots have been shown to have great potential to attract attention of children with ASD and can facilitate early interventions on core deficits. In this paper, we propose a robotic platform that mediates imitation skill training for young children with ASD. Imitation skills are considered to be one of the most important skill deficits in children with ASD, which has a profound impact on social communication. While a few previous works have provided methods for single gesture imitation training, the current paper extends the training to incorporate mixed gestures consisting of multiple single gestures during intervention. A preliminary user study showed that the proposed robotic system was able to stimulate mixed gesture imitation in young children with ASD with promising gesture recognition accuracy.