In this Letter, we report the discovery of an intriguing hypervelocity star (HVS; J1443+1453) candidate that is probably from the Sagittarius Dwarf Spheroidal galaxy (Sgr dSph). The star is an old and very metal-poor low-mass main-sequence turn-off star (age similar to 14.0 Gyr and [Fe/H] = -2.23 dex) and has a total velocity of 559.01(-87.40)(+135.07) km s(-1) in the Galactic rest frame and a heliocentric distance of 2.90(-0.48)(+0.72) kpc. The velocity of J1443 +1453 is larger than the escape speed at its position, suggesting that it is a promising HVS candidate. By reconstructing its trajectory in the Galactic potential, we find that the orbit of J1443+1453 intersects closely with that of Sgr dSph 37.8(-6.0)(+4.6) Myr ago, when the latter has its latest pericentric passage through the Milky Way. The encounter occurs at a distance 2.42(-0.77)(+1.80) kpc from the center of Sgr dSph, a distance that is smaller than the size of the Sgr dSph. The chemical properties of this star are also consistent with those of an Sgr dSph-associated globular cluster, or of the Sgr stream member stars. Our finding suggests that J1443+1453 is an HVS that is either tidally stripped from the Sgr dSph or ejected from the Sgr dSph by the gravitational slingshot effect, requiring a (central) massive/intermediate-mass black hole or a (central) massive primordial black hole in the Sgr dSph.