For 錢應該花在刀口上。刀口…… and spending money. How is spending money related to 刀口?
Look here: http://www.zdic.net/c/0/3f/99108.htm
刀口 means the right spot 花 means spend
钱要花在刀口上 You should spend/use your money where it is most needed.
After some more research, I found out a reason why that phrase can make sense. There is a saying:
When you have high quality steel, use it to make the blade of the sword
then "錢應該花在刀口上" is a variant of the saying above. Maybe it can mean, when you have limited money to improve a sword, spend it on the sword's blade (instead of on the handle or on the scabbard).
There is another idiom in Chinese culture：
Literally, it means one spend one dollar as two dollars. It is usually used to describe that kind of people who are shrewd in money matters。
So,I think the connection between money and 刀口 is because if you intend to 一分钱当两分钱花, then you have to cut one dollar into halves.
By the way, we usually say 刀刃 rather than 刀口。 But the two words have basically the same meaning.