Is there an approach to save the whole simulation results in Modelsim

You can add "log -r *" to your .do file before your simulation "run" command. This will create a vsim.wlf that can be opened up later in the GUI to view all the simulation waveforms. However, if you are running very long simulations or have a very large design this might require a lot of disk space. In that case, you can replace the "*" with a particular hierarchal hdl path from your design.