Many cactus' have cells present called sclereids. Sclereids are lignified (contains lignin, a substance similar to fibre) cells which are often very tough and gritty. Pears have tons of sclereids as well, which gives them that characteristic gritty texture.
I thought it would be something like this. It really makes a lot of sense, the abrasives cactus are there but unlike paper they are suspended in the fruit (fruit?) like a good polish and can work on the rust more effectively. I really think that the best way to remove rust is a physical process (sanding, grinding, polishing) rather than a chemical one.
Now that you've asserted your "intellectual dominance" over the rest of us non-chemists, can we get a layman's terms version?

lol It is sort of fun to apply my chemistry knowledge to a knife problem.
basically if you take the cactus and grind it up in a mortar and pestle then put it in water to make a solution (this is so you can test the pH easier) you can test with strips or a special chemical called litmus (or any indicator). An indicator
indicates wether a substance is a acid, base, or neutral.
Now in my example I was using HCl or hydrochloric acid. This is a strong inorganic acid and therefore has a high disassociation rate. The juice in the cactus would be an weak acid like orange juice ( this is why when you drink orange juice it does not melt your teeth). This is something that I forgot about.
Side reactions often occur with acid resulting in rust. Think of what happens when your car gets hit by acid rain...turns into a rust bucket
Right. In the example I gave the products were FeCl[SUB]2[/SUB] and H[SUB]2[/SUB]O. Now this would be the reaction just with the rust and would give you a salt and water. Without doing a test I think that the salt would be in an liquid state ( technically called aqueous) so therefore it could be removed. But yes the side reactions. Many metals when submerged into HCl dissolve and give off hydrogen gas (example: Mg (s) + HCl (aq) --> MgCl[SUB]2[/SUB] (aq) + H[SUB]2[/SUB] (g) ) So if you used hydrochloric acid to remove rust you would most likely dissolve your whole knife blade into the solution of acid

So yes there are side reactions as well and I am sure I have forgotten (and am too lazy) about many reactions that would also take place here.
I'm watching this thread to see if the cactus juice really removes rust.
I really think that it is more the physical structure of the cactus than the juice but it will be interesting to find out