Seeking strategies to enhance the overall combinations of mechanical properties is of great significance for engineering materials, but still remains a key challenge because many of these properties are often mutually exclusive. Here we reveal from the perspective of materials science and mechanics that adaptive structural reorientation during deformation, which is an operating mechanism in a wide variety of composite biological materials, functions more than being a form of passive response to allow for flexibility, but offers an effective means to simultaneously enhance rigidity, robustness, mechanical stability and damage tolerance. As such, the conflicts between different mechanical properties can be "defeated" in these composites merely by adjusting their structural orientation. The constitutive relationships are established based on the theoretical analysis to clarify the effects of structural orientation and reorientation on mechanical properties, with some of the findings validated and visualized by computational simulations. Our study is intended to give insight into the ingenious designs in natural materials that underlie their exceptional mechanical efficiency, which may provide inspiration for the development of new man-made materials with enhanced mechanical performance. STATEMENT OF SIGNIFICANCE: It is challenging to attain certain combinations of mechanical properties in man-made materials because many of these properties - for example, strength with toughness and stability with flexibility - are often mutually exclusive. Here we describe an effective solution utilized by natural materials, including wood, bone, fish scales and insect cuticle, to "defeat" such conflicts and elucidate the underlying mechanisms from the perspective of materials science and mechanics. We show that, by adaptation of their structural orientation on loading, composite biological materials are capable of developing enhanced rigidity, strength, mechanical stability and damage tolerance from constrained flexibility during deformation - combinations of attributes that are generally unobtainable in man-made systems. The design principles extracted from these biological materials present an unusual yet potent new approach to guide the development of new synthetic composites with enhanced combinations of mechanical properties.