What does the expression cut the odds in the context of betting mean?
The complete phrase is
While we're not sure what is going on in Greece, it is safer for us to suspend betting rather than keep cutting the odds. (as found here).
It means to reduce the odds. In the previous paragraph, they explain that the odds had been 4-6 but were cut to 1-3.
Outside of that kind of context (where you're talking about odds literally), the phrase can also mean to take action that would reduce the odds. So for example you may change your diet to cut the odds of a heart attack.
Originally, the odds (of a good result) were 4-6, or 40% This equals 4/(4+6)= 4/10.
The new odds of a good result, as quoted, are 1-3 or only 25%. (1/(1+3)=1/4.
The odds are falling, and FAST, heading toward zero. Things got to the point where even the "bookmaker" didn't want to quote even worse betting odds. So they suspended the betting.