We demonstrate a selective microcleaving graphene (MG) transfer technique for the transfer of graphene patterns and graphene devices onto chosen targets using a bilayer-polymer structure and femtosecond laser microfabrication. In the bilayer-polymer structure, the first layer is used to separate the target graphene from the other flakes, and the second layer transfers the patterned graphene to the chosen targets. This selective transfer technique, which exactly transfers the patterned graphene onto a chosen target, leaving the other flakes on the original substrate, provides an efficient route for the fabrication of MG for microdevices and flexible electronics and the optimization of graphene's performance. This method will facilitate the preparation of van der Waals heterostructures and enable the optimization of the performance of graphene hybrid devices.