Te see what te desconozco means, let’s look at the prefix -des.
The prefix des- usually means opposite. For example, acuerdo = agreement, desacuerdo = disagreement. Or it may refer to some kind of undoing or reversing of a process: taparlo = cover it (with a lid), destaparlo = uncover it.
However, in some cases the precise sense of oppositeness conveyed by -des is idiosyncratic. You might think that desconocer simply means not knowing something, but it seems to include the idea of your having been expected to know something that you don’t. Te desconozco = I thought I knew you (well), but now I see that I don’t. You could use it when someone does something you thought they weren’t capable of, for example, when their hidden talent for juggling is revealed — and in this case you could also call them un estuche de monerías (a person of many talents) — or when you learn that your true love is actually a patán, breaking your heart. You surprise me or I had no idea that you … captures the idea nicely.