How close would the sun have to get to a supermassive black hole to have Jupiter stripped and slingshot into interstellar space? Please make whatever assumptions are needed.  Assume sun approaches black hole on some sort of hyperbolic trajectory.  Assume size of supermassive black hole is same as the one at center of our galaxy.  How close would sun have to get in order for Jupiter to be “slingshot” into interstellar space.
Closer than about 10000AU, 1.5 trillion km or about 2000 times the orbital radius of Jupiter.

Three body systems are peculiar beasts, and but I'm going to change the question to "Would Jupiter be in a stable solar orbit?" This makes it a question of Hall radius.

The Hall radius is $r_H = a\sqrt[3]{m/3M}$ where $m/M=1/4000000$ is the ratio of solar mass to black hole mass (the mass of Jupiter is treated as negligible!) and $a$ is the orbital distance of the sun about the black hole

If we set $r_H$ to 5 (AU) and solve for $a$ we get a value of about 10000  (I'm only working at 1 s.f. accuracy here. In other words, if the sun is orbiting the black hole at 10000AU then Jupiter would be in a marginally stable orbit.  If the sun got closer than 10000AU then Jupiter would tend to orbit the black hole and not the sun.

However this is only an upper bound. On a hyperbolic orbit the sun would spend little time near the black hole and so even if Jupiter had drifted in the black hole's gravity as the sun passed by, as the sun and jupiter moved away, it would tend to fall back into orbit around the sun. To model whether Jupiter would actually be lost would require knowledge of the initial conditions and numerically solving the differential equations of motion.