purpose of saw filter

All of the mobile phones do use one or more SAW filters in the design.
Why can't we use another filters?

SAW filter is small and very sharp. That why it uses in cell phones. However, it is very high input/output impedance. You migh try to compare the size of a 245MHz helical filter and SAW filter. you will see the big difference

the most important purpose of SAW filter is to reject the IF mirror signal in the receiver. It is usually small and shape so it is easily adopted in mobile phone. But in more advanced phone receivers archtecture such as direct conversion, Saw is often eliminated to cut down cost and save PCB area.

I think this attached article gives some useful info on SAW BPF

SAW filters are used today in mobile phones as RF preselection filters. Immediately after the antenna and switches, but before LNA. The goal is to preselect the system band and to improve blocking performance of the receiver. IF SAW filters are no more used, particularly in GSM cellular phones, because superheterodyne receiver architectures are replaced by direct conversion. SAW filters are extremly small sized in particular at RF frequencies in GHz region and still decreasing in size. In the last time FBAR (BAW) are also introduced (e.g. Agilent).

Added after 6 minutes:

I think this attached article gives some useful info on mobile phones related SAW filters.