Magnetically actuated miniature soft robots are capable of programmable deformations for multimodal locomotion and manipulation functions, potentially enabling direct access to currently unreachable or difficult-to-access regions inside the human body for minimally invasive medical operations. However, magnetic miniature soft robots are so far mostly based on elastomers, where their limited deformability prevents them from navigating inside clustered and very constrained environments, such as squeezing through narrow crevices much smaller than the robot size. Moreover, their functionalities are currently restricted by their predesigned shapes, which is challenging to be reconfigured in situ in enclosed spaces. Here, we report a method to actuate and control ferrofluid droplets as shape-programmable magnetic miniature soft robots, which can navigate in two dimensions through narrow channels much smaller than their sizes thanks to their liquid properties. By controlling the external magnetic fields spatiotemporally, these droplet robots can also be reconfigured to exhibit multiple functionalities, including on-demand splitting and merging for delivering liquid cargos and morphing into different shapes for efficient and versatile manipulation of delicate objects. In addition, a single-droplet robot can be controlled to split into multiple subdroplets and complete cooperative tasks, such as working as a programmable fluidic-mixing device for addressable and sequential mixing of different liquids. Due to their extreme deformability, in situ reconfigurability and cooperative behavior, the proposed ferrofluid droplet robots could open up a wide range of unprecedented functionalities for lab/organ-on-a-chip, fluidics, bioengineering, and medical device applications.