My tire was slashed. Replaced the inner tube, but should I replace the tire as well?
You already know the answer to this question.
Slashes in the sidewall tend to open up as the pressure from inner tube is pushing the tire further apart. If you're lucky you might escape with a simple pinch flat. More serious problems include:

the inner tube pushing through the sidewall rubbing on the frame or fork causing the inner tube to burst like a balloon.
the inner tube removing the bead of the tire

Either of these I wouldn't want to happen at speed.