Graphene has recently attracted much interest as a material for flexible, transparent electrodes or active layers in electronic and photonic devices. However, realization of such graphene-based devices is limited due to difficulties in obtaining patterned graphene monolayers on top of materials that are degraded when exposed to a high-temperature or wet process. We demonstrate a low-temperature, dry process capable of transfer-printing a patterned graphene monolayer grown on Cu foil onto a target substrate using an elastomeric stamp. A challenge in realizing this is to obtain a high-quality graphene layer on a hydrophobic stamp made of poly(dimethylsiloxane), which is overcome by introducing two crucial modifications to the conventional wet-transfer method - the use of a support layer composed of Au and the decrease in surface tension of the liquid bath. Using this technique, patterns of a graphene monolayer were transfer-printed on poly(3,4-ethylenedioxythiophene):polystyrene sulfonate and MoO3, both of which are easily degraded when exposed to an aqueous or aggressive patterning process. We discuss the range of application of this technique, which is currently limited by oligomer contaminants, and possible means to expand it by eliminating the contamination problem.