As with franko's answer, the reason why you use salt (preferably sea salt) is that it helps to crush and mince the garlic whilst you are chopping.
If you are worried about too much salt in your diet, then do not use any other salt than what is used whilst mincing your garlic.
Like above, I don't understand why you have to discard what is on the knife
, I am assuming that you have peeled your clove.
If you are worried about cutting yourself, simply scrape the side of the knife on the edge of the board, gather it up into a little pile and carry on mincing, a bit of chop chop, then scrunch down with the sea salt.
As an aside to this, though this was always my preferred method in the past, I have now taken to grating garlic with the very fine part of a cheese grater.
This not only takes a second or two but also you don't have to peel your clove as the skin is left on the top side of the grater, whilst the grated garlic is on the underside.
cooking.stackexchange.com/users/53089/dougal 5.0.0
I have read that sprinkling some salt on the minced garlic as you chop helps alleviate the sticking, but you may not want extra sodium in your recipe.
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I've found that using either (a) frozen minced garlic or (b) adding a little oil to the garlic both work pretty well.
cooking.stackexchange.com/users/17216/david
Why not simply get a Garlic Press and make things easy on yourself?
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If the problem is readily minced garlic sticking to the knife, this is hard to solve (some pros seem to avoid it by using very high chopping speeds leaving no time for anything to stick).
To get (properly) minced garlic off the knife, a plastic(!!!)
scraper card is very handy.
If uneven mincing due to big lumps being stuck to the knife is to be avoided: Actually dicing the clove (board parallel cuts 9/10 of the length, lengthwise 9/10, then slicing) will deal with that, at the cost of wasting (or having to re-chop) an end piece.
Also, this can get time consuming if you need to prep a whole head worth of garlic...
cooking.stackexchange.com/users/35312/rackandboneman
Whenever I mince cloves of garlic on a cutting board, it sticks to the sides of the knife making it a tedious task? Is there anyway to prevent this from happening when using a knife to mince garlic the old-fashioned way? Otherwise, I frequently have to wipe off the garlic remnants from the sides of the knife.
How to mince garlic efficiently without the garlic sticking to the sides of the knife?
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cooking.stackexchange.com/users/54195/nhunsaker
Adding salt or oil can reduce sticking, or you can use frozen minced garlic or chop faster to reduce the time for anything to stick. The easiest solution is probably to get a garlic press. There are a number of ways recommended to stop garlic sticking to the knife when chopping. These include sprinkling the garlic with saly or a little oil or chopping at high speed. Another option would be to buy a garlic press.
Sprinkling with salt, adding oil or chopping at high speed prevent garlic from sticking to the knife. Buy a garlic press.