Prosecutors further claim Visser, from Milton Bridge, Midlothian, isolated the woman from family and friends and was physically violent.
A fourth charge says he engaged in a course of abusive behaviour against the woman on various occasions.
The accusation lists a total of 26 different claims.
A number of them are similar to the threatening behaviour allegation, but also include a string of sexual matters.
One is that he sent an intimate image of the woman to someone else.
The indictment goes on to state that the prosecution may present evidence about other matters dating back to 2004, but these are not formal charges at this stage.
They feature claims of physical and sexual incidents, threats and controlling behaviour.
At the High Court in Glasgow, Ian Duguid, defending, said: “It is a plea of not guilty to the indictment.”
A trial was set for 12 January 2028 in Edinburgh.
The ex-rugby star was born in the Netherlands, but opted not to play for his home nation.
Instead he represented Scotland as a winger between 2012 and 2017 before he retired from the sport two years later.
