At present, the existing vegetable grafting machines are cutting and grafting operations for a single plant or row. They need to manually or automatically grab the seedlings, and their grafting efficiency is not significantly higher than that of manual grafting techniques. In this paper, grafted melon seedlings were the subject of the research. Based on the splice-grafting method, we designed a clamping and positioning device for full-tray seedlings and a mechanical device to realize full-tray grafting by locating the vegetable seedlings and completing the full-tray grafting process without damaging the seedlings. The results show that the cutting success rate for pumpkin rootstock and for melon scion reached 100% and 92%, respectively. The lengths of the long axis of the section of the rootstock and the scion were 6.2–7.7 mm, and the cutting angle was maintained at 30 degrees, thereby able to meet the requirements of the grafting method. The average grafting efficiency for the rootstock and scion were 2134 plants/h, and the average grafting success rate was 67%.