Supermassive black holes (SMBHs) can capture and tidally disrupt stars or substellar objects orbiting nearby. The detections of Sw J1644+ 57-like events suggest that at least some TDEs can launch a relativistic jet beaming toward Earth. A natural expectation would be the existence of TDEs with a relativistic jet beaming away from Earth. The nearby TDE candidate IGR J12580+ 0134 provides new insights into the jet phenomenon. Combining several constraints, we find that the event invokes a 8− 40 Jupiter mass object tidally disrupted by a SMBH. Recently, a bright radio transient was discovered by Irwin et al. in association with IGR J12580+ 0134. We perform detailed modeling of the event based on a numerical jet model previously developed for the radio emission of Sw J1644+ 57. We find that the radio data of IGR J12580+ 0134 can be interpreted within an external forward shock model in the Newtonian regime. Using Sw J1644+ 57 as a template and properly correcting for its luminosity, we argue that the observed X-ray flux in early times is too faint to allow an on-beam relativistic jet unless the Lorentz factor is very small. Rather, the X-ray emission is likely from the disk or corona near the black hole. From various constraints, we find that the data are consistent with an off-beam relativistic jet with a viewing angle of and an initial Lorentz factor of a few. This scenario can readily be tested in the upcoming very long baseline interferometry observations.