Tazeen Yes, you can buy a Saver Day Pass from Bern to Zermatt.
This pass is not valid for cable cars or the Gornergrat train. It is not valid on the next day, you have to buy a new pass or ticket. It is not exchangeable or refundable. You can use every train between Bern and Zermatt on the date you selected, without other ticket or seat reservation.
It is not possible to say if this pass is cheaper as tickets, the price is not fix and vary, depending on the demand and the date of the purchase.
You have also Supersaver Tickets who could be cheaper as the pass, but you must use only the selected trains.
With Point-to-point Tickets, you can use every train on the selected day for one way.