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The 3 types of cone cells in normal humans allow them to view 3 types of colors and any color made from mixing and matching those 3.

So, 2 types of cone cells should only allow to view just 2 types of colors and any colors made from those two.

But that is clearly not the case.

https://en.wikipedia.org/wiki/Color_blindness#Red.E2.80.93green_color_blindness

Protanopes, deuteranopes, and tritanopes are dichromats; that is, they can match any color they see with some mixture of just two primary colors (whereas normally humans are trichromats and require three primary colors).

Also, from personal experience, I'm colorblind and can see and differentiate all 3 red, green, and blue. It's just the hues between red-green and green-blue I can't distinguish much...

How exactly do dichromats see all three colors when they lack one type of cone cell?

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Cones do not literally interpret colors. The three cones work together to encode a signal that is abstractly interpreted by your brain in higher processing centers. Here is what neuroscientists currently think the decoding scheme looks like:

This leads to what's called opponent process, an antagonist mechanism whereby the perception of green/red are a matter of the contrast between the two. In a deuteranopes, the mechanism of antagonism is missing, so the colors can not be differentiated.

What this implies is that (to some extent) a single color has no meaning. Colors are only meaningful in the context of other colors.

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    $\begingroup$ Based on that decoding scheme, the problem of green/red colourblindness (assuming lack of "green" cones) should be that there is a lack of information in green and red areas. For both the only signal would be low levels of "red" stimuli (since the overlap of "green" stimuli is missing). However, this should also cause multiple correspondence pairs along the "red" stimuli curve (light green to dark orange; yellow to orange etc) at similar levels of "red" stimuli. Is this the case in green/red colourblindness? I thought that only green and red were mixed up. $\endgroup$
    – fileunderwater
    Aug 7, 2013 at 15:02
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    $\begingroup$ The decoding scheme is direct measurement of cone activity in the presence of light. But how the higher processing centers interpret signals from the cones is not as straightforward as you might imagine; it's actually still an open question! Opponent process is a current theory about how it works, but the experiments consist of more psychology than neuroscience so we're on the outside looking in. But notice that the evidence suggests that R-G relies on only two cones, while Y-B relies on all three. So there's probably some loss in YB, but not to the point where you can't differentiate them. $\endgroup$
    – Keegan Keplinger
    Aug 8, 2013 at 14:19

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