I am trying to find the number of knife deaths and/or knife attacks by country per year. There are many sources for gun deaths, but strangely not any that I could find for knife deaths.
You can download crime/murder statistics that are classified by "mechanism" from the United Nations Office on Drugs and Crime.
On the left menu sidebar, choose "Crime and Criminal Justice"
Then select "Homicide"
Then select "Percent of homicides by mechanism (2005-2012)
Create an XLS export (here's a direct link)
The term they seem to use is "Sharp" for knife deaths
Note that there are some other potential categories, so you may find better data sets by digging around.