Any good stationery shop will have the cutting mats which you use an ordinary blade to cut (together with a metal ruler).
If you want a proper paper cutter (integrated mat and cutter) then the stationery shop on the 2nd floor of Funan Centre has a good selection - price ranging from $40 to $200 depending on size and brand.
Stationery shops do sell cutting boards. I bought an A4 size version for $120. The sliding type not the chopping type. The chopping type is cheaper but I have forgotten how much.
Look in at Big bookshop at clementi if its convenient for you. They got that guillotine kinda cutter, which u can use to chop your paper/photos with gusto, and accuracy. Just be careful with your own fingers tho'...