Umm - I had to Google this because everything I've heard is the opposite of what you've heard.
No salt - it makes the soil resistant to water penetration
Don't over-harvest - it reduces the next year's yield
Don't use a knife - it can spread disease
Here is what I found (with the links) that backs up what I've heard:
Do not use salt as a weed killer. It will not harm the asparagus, but it inhibits water penetration in the soil. Also, rains can leach the salt out of the asparagus bed and into the rest of the garden, injuring other vegetables that are less salt tolerant than asparagus.
http://www.hort.purdue.edu/hort/ext/Pubs/HO/HO_096.pdf
You may hear of using common salt to kill weeds in asparagus, but cultural methods along with limited, careful use of herbicides is preferred. A build-up of salt in the soil is not desirable; the only reason it doesn't harm the asparagus is that their roots are buried so deeply in the ground.
http://www.extension.umn.edu/yardandgarden/ygbriefs/H204asparagus.html
Common rock salt was once used to control shallow-rooted weeds in asparagus because asparagus is deep rooted and can tolerate some salt. However, this is no longer recommended because the salt can damage soil structure by creating a crust that impedes water infiltration.
http://extension.missouri.edu/explore/agguides/hort/g06405.htm
The yield of asparagus spears in the spring is directly related to the previous year's fern growth. Asparagus can be harvested for a limited time (two weeks) the second year after planting crowns (three years from seed transplants). Overharvesting one year can weaken the plant and decrease yields the following year… Asparagus spears are best harvested by snapping them off by hand near ground level. Most growers prefer to snap the asparagus spears when they reach 7 to 9 inches in length in cool weather (less than 70 degrees Fahrenheit), and the spear tip is tight or 5 to 7 inches in warmer weather (more than 70 degrees). Snapping will break the spear cleanly at a tender point. Cutting with a knife is generally not recommended because it may spread diseases from plant to plant.
http://extension.missouri.edu/explore/agguides/hort/g06405.htm