Question

Can we get rid of all voltages in the circuit when we are trying to find thevenin resistance?

Answer 1

While I am not certain I understand the question, a tentative answer is no, if you are trying to calculate the resistance in a circuit you need something to fill in the equation \[V=IR\]

Answer 2

Do you know about thevenin equivalent ?

Answer 3

I believe so, where you take a "blackbox" circuit and create a Thevenin's equivalent. So your question then is can you ignore voltages when calculating the equivalent resistor, yes.