Rapid and sustained condensate droplet departure from a surface is key toward achieving high heat-transfer rates in condensation, a physical process critical to a broad range of industrial and societal applications. Despite the progress in enhancing condensation heat transfer through inducing its dropwise mode with hydrophobic materials, sophisticated surface engineering methods that can lead to further enhancement of heat transfer are still highly desirable. Here, by employing a three-dimensional, multiphase computational approach, we present an effective out-of-plane biphilic surface topography, which reveals an unexplored capillarity-driven departure mechanism of condensate droplets. This texture consists of biphilic diverging microcavities wherein a matrix of small hydrophilic spots is placed at their bottom, that is, among the pyramid-shaped, superhydrophobic microtextures forming the cavities. We show that an optimal combination of the hydrophilic spots and the angles of the pyramidal structures can achieve high deformational stretching of the droplets, eventually realizing an impressive "slingshot-like" droplet ejection process from the texture. Such a droplet departure mechanism has the potential to reduce the droplet ejection volume and thus enhance the overall condensation efficiency, compared to coalescence-initiated droplet jumping from other state-of-the-art surfaces. Simulations have shown that optimal pyramid-shaped biphilic microstructures can provoke droplet self-ejection at low volumes, up to 56% lower than superhydrophobic straight pillars, revealing a promising new surface microtexture design strategy toward enhancing the condensation heat-transfer efficiency and water harvesting capabilities.