Considering that most of the groups that use 'communism' as a buzzword for evil...tend to be right wing

If you're including "right wing" instead of just "far right" this quickly sounds like "people with normal political beliefs can't raise objections." It's not reasonable to frame the realm of reasonable opinion in that way.

The reason why "right wing" groups get to use communism as a buzzword for evil (and the reason mainstream left wing organizations have an incredibly shameful history of early/mid 20th century Stalinist apologetics) is because everyone agrees communism is a left wing ideology and "communism-as-practiced-by-self-described-marxist-states" was basically a left wing phenomena (especially since there's also a general agreement on what left wing means substantially in terms of weltanschauung). They take the 20th century "communist" states as evidence in support of their views which are aligned against the far left in more ways than being against communism-as-marxist-ideal. This is especially true if one believes that "establishing communism"

The issue is that saying 'Communism is tyranny', implies that the entire point and ideological motivations of communism is to establish tyranny and oppress the people.

Yes, the belief should be mocked. They're rewording and redefining what an ideology actually is

This isn't a new innovation created by right wing ideologues to smear the left. It's a constant feature of these debates and needs to be engaged with. "no true communism" might be able to defeat objections but it needs to engage with "look at what far left wing governments and actions mean in practice" style arguments.