In response to the practical production challenges posed by the unreliable operation of the V-shaped squeezing soil-covering and -pressing device (VCP) for planters under clay soil conditions in Northeast China, incomplete seed furrow closure, and severe soil adhesion on pressing wheels, this study proposes a device with star-toothed concave discs for soil-covering and -pressing (STCP) with the aim of enhancing the soil-covering quality of planters. The main working principles of STCP were expounded, and its main structural and installation parameters were determined and designed. Based on bionics, with the dung beetle’s protruding head structure as the research object and UHMWPE as the material, an optimized protuberance-type bionic pressing wheel was designed. A Box–Behnken experiment was conducted by taking the width of the compression wheel, the spring deformation, and the installation angle as experimental factors, as well as the weight of the soil adhered to the surface of the pressing wheel (SW) and the soil compactness (SC) as the evaluation indicators. The optimal structural parameters of the pressing device were determined as follows: the width of the pressing wheel was 60.57 mm, the spring deformation was 55.19 mm, and the installation angle was 10.70°. The field comparison tests of soil covering performance showed that the star-tooth concave disc soil-covering device can effectively solve the problem of seed “hanging” and “drying”. The average covered soil weight of the star-tooth concave disc soil-covering device was 241.46 g, and the average covered soil weight of VCP was 223.56 g. Compared with VCP, the average covered soil weight of STCP increased by 8.01%. The variation coefficient of covered soil weight after the operation of the star-tooth concave disc soil-covering device was 3.71%, which was more uniform than VCP. The field comparison tests of soil-covering thickness showed that the uniformity of soil-covering thickness can be significantly improved by adding a star-tooth concave disc soil-covering device to VCP. The comparative tests of soil anti-adhesive showed that the convex hull type pressing wheels optimized by bionics had better soil anti-adhesive performance, and the soil adhesion weight was reduced by 43.68% compared with VCP. The field comparative tests of seedling emergence showed that the seedling emergence rate after STCP operation was 3.9% higher than that of VCP.