No. You can trip someone else, but you can only stumble (yourself), and it suggests an accident.
If someone else deliberately trips you, use that form: he tripped me.
You can trip or stumble. I don't see much difference when it refers to, for example, a rock in your path. Perhaps -- I wonder if others see it the same -- if you stumble, you catch yourself before you fall, but when you trip, you may fall to the ground.
I stumbled over the uneven cobblestones and almost fell.
I tripped over the uneven cobblestones and bruised my knee.
Student or Learner