How can I perform progressive collapse analysis (e.g. remove column and get dynamic response) in SAP2000?

You can simulate the progressive collapse analysis with dynamic effects by running time history analysis as follows:

(1) Create "Model A" that contains the entire structure, including the column to be removed. Analyze Model A to obtain internal forces for the column to be removed.

(2) Create a "Model B" that does not contain the column to be removed. However, simulate the presence of column to be removed by applying end column forces obtained from Model A to the appropriate joints of the model.

(3) Run time history analysis with a load applied at time = 0. The load would be opposite to that applied in step 2 and it would effectively simulate removing the column. You would need to use a ramp function to reduce the loads applied in the time history analysis to zero values in a short time. How short (or long) the time should be would depend on how quickly the column is removed and you should use your judgment to decide this.