There's a big difference between "this causes cancer" and "this causes lots of cancer". IARC look at the quality of the evidence to put things into one of four groups. Some things definitely do cause cancer, but they don't cause very much cancer.

Don't forget that there are several multi-billion dollar companies who sell aspartame who are vigorously campaigning to promote the safety of their products. It's entirely unsurprising that the data is unclear when you have that level of interference in the research. It's also really tricky to do diet research on humans - we can't lock people up for a year to give them a controlled diet, so we end up asking them to write down what they've eaten and drunk. This means the data researchers have is pretty bad. Looking for a small signal in very noisy data is hard.