Lots of mice studies don't translate well into humans. This one is highly specific -- a specific mutation. It's unlikely to have much bearing on real world cancer.
I have to say, the very first thing that came to mind when I read the article was Xkcd: http://www.xkcd.com/1217/
"To test the effect of vitamin C, two million HCT116 or VACO432 cells were injected subcutaneously into the flank of 6 to 8-week-old female athymic nude mice (Harlan, Indianapolis, IN). After 7-10 days, mice with tumors of 40-60 mm3 were randomly divided into two groups. One group was treated with freshly prepared vitamin C (sodium ascorbate in 400 ul PBS, 4 g per kilogram of body weight) by intraperitoneal (IP) injection twice a day (HCT116: n=6, VACO432: n=6). Control group mice were treated with PBS instead of vitamin C with the same dosing schedule (HCT116: n=4, VACO432: n=7)."
[...]
[Caption Fig 2:]
"Tumor sizes were measured 2-3 times per week in an unblinded manner."
http://www.sciencemag.org/lookup/doi/10.1126/science.aaa5004
Not only are they mice, but they have no immune system[1]. Also, the dose of vitamin C is like consuming an entire bottle twice a day (~240 g)[2]. They are honest about the lack of blinding, which is good, but obviously that should make us wary of these findings. Also, they do not report tumor size before splitting into treatment vs control groups (only saying mice with 40-60 mm^3 tumors were used). Put the larger ones in the control group and you can easily appear to be slowing tumor growth for totally artefactual reasons.
For example, start with low initial (40) and high initial (60) cells in two different mice. If the cells all divide every day how many do you expect after 1:3 days. Low: 40,80,160; High: 60,120,240; Difference: 20,40,80. The difference seems to grow just due to the starting conditions, growth rates were the same. So these results are uninterpretable without knowing the starting tumor sizes.
[1] https://en.wikipedia.org/wiki/Nude_mouse
[2] http://www.allergyresearchgroup.com/buffered-vitamin-c-240-g...
This is a perfect example of what is wrong with biomed research. Just because the null hypothesis of no difference is rejected does not mean it is for your favorite reason. There are other reasons for this difference. For example, as mentioned above, perhaps the initial tumor size was different (which we cannot see since the size of the points in figure 2 correspond to ~50 mm^3 on the y axis).