Plasma jets are ubiquitous in space. In geospace, jets can be generated by magnetic reconnection. These reconnection jets, typically at fluid scale, brake in the near-Earth region, dissipate their energies, and drive plasma dynamics at kinetic scales, generating field-aligned currents that are crucial to magnetospheric dynamics. Understanding of the cross-scale dynamics is fundamentally important, but observation of coupling among phenomena at various scales is highly challenging. Here we report, using unprecedentedly high-cadence data from NASA's Magnetospheric Multiscale Mission, the first observation of cross-scale dynamics driven by jet braking in geospace. We find that jet braking causes MHD-scale distortion of magnetic field lines and development of an ion-scale jet front that hosts strong Hall electric fields. Parallel electric fields arising from the ion-scale Hall potential generate intense electron-scale field-aligned currents, which drive strong Debye-scale turbulence. Debye-scale waves conversely limit intensity of the field-aligned currents, thereby coupling back to the large-scale dynamics. Our study can help in understanding how energy deposited in large-scale structures is transferred into small-scale structures in space.