砍 literally means to chop with an axe — so 砍价 is "hacking the price down." The image is vivid and very Chinese: the seller starts high, you chop chunks off the price until you both stop swinging.
culture
Bargaining is expected at outdoor markets, tourist stalls, and small electronics bazaars in China — but NOT at supermarkets, malls, or chain restaurants where prices are fixed (明码标价). A common opening move is to offer 30–50% of the asking price.