As long as the out of date mayonnaise has been refrigerated once opened and it doesn't smell bad then the out of date mayonnaise is still safe to eat.
If the mayonnaise has been kept sealed then it can last up to a year and sometimes longer past the sell by date or expiration date.
The mayonnaise loses it's freshness once the sell by or use by date passes but it's usually very safe to eat unless it has started to smell bad.
If the mayonnaise is bad enough to make you sick then you'll notice a very bad smell to it such as rotten egg smell since mayonnaise usually contains raw eggs in the ingredients.
If the mayonnaise doesn't smell bad or hasn't grown any mold on it then eating the out of date mayonnaise is perfectly safe and okay.
Also bad mayonnaise will also smell bad too.
If you're in doubt about whether the out of date mayonnaise is bad or not then just throw it away and get some fresh mayonnaise.