The issue has come to the fore following Liverpool striker Luis Suarez's clear dive at the weekend, after which Stoke boss Tony Pulis called for players adjudged to have been guilty of simulation to be banned for three matches.
The Football Association does not currently allow players to be punished for diving retrospectively however - referees can only show a yellow card at most - but Boyce, Britain's representative on FIFA, believes all associations should.
Boyce told Press Association Sport: "I have seen several incidents recently, and I watched the latest Suarez incident two or three times, and to me it is nothing less than a form of cheating.
"It is becoming a little bit of a cancer within the game and I believe if it is clear to everyone that it is simulation then that person is trying to cheat and they should be severely punished for that.
"It can be dealt with retrospectively by disciplinary committees, and it is done so in some associations, and I believe that is the correct thing to do.
"It can at times be very, very difficult for referees to judge whether something is a foul or a fair tackle and if players are diving then it makes their job even harder."
The issue has been discussed by the FA and the leagues before without any change in policy. The Premier League have previously suggested a three-man panel to review contentious incidents after every weekend, which could include simulation, and would be open to renewing discussions on bringing in such a system.
The FA said the issue was often reviewed. A spokesman added: "Simulation is not something that the FA currently take retrospective action over but it is an issue that is often reviewed and discussed by the game's stakeholders."
Liverpool boss Brendan Rodgers on Monday leapt to the defence of Suarez, saying: "At this moment there seems to be one set of rules for Luis and another set for everyone else.
"Diving and simulation is obviously a wider issue in football and one that we all agree has to be eradicated from our game but there were other incidents this weekend that didn't seem to generate the same coverage.
"I believe some people need to develop a sense of perspective and I also believe in this moment the vilification of Luis is both wrong and unfair."