there is that slight variation of 懂 and 明白. both mean understand but with 明白 it also means clear.
in this case using 懂 is more suited to your need.
but to clarify things, in terms of "know" do you mean listen? to speak? or to read and write, it would be better to specify in the sentence but for general understanding type, 我不太懂普通话 is fine