Is removing poorly predicted data points a valid approach?
The process you described is not valid, it is almost certainly overfitting. However the overall idea may very well be valid. What you should do instead is take a portion of your dataset as the testing which is not looked at during algorithm development, and split the rest between training and validation sets however you please.

Looking only at the training and validation sets, develop your entire end to end algorithm, including the classifier!

Once you are happy with the algorithm, try running it on the test set to get a more accurate measure of performance.