I have a set of polygon features that I would like to split into different groups/clusters based on the distance attribute provided in the attribute table, using arcgis geoprocessing tools as far as possible (as I am inexperienced in Python). I have tried to use the clustering tools available (i.e. grouping analysis) but they do not appear to have the function that I require, especially when I would like the tool to run through the features starting with the shortest distance value. In addition, I would like to create the grouping/clustering such that once a polygon is grouped/clustered, it will no longer be considered for further grouping/clustering.
base on your table, your data are already grouped by their distance values. You could simply use a reclass, beginning with the lowest grouping and proceeding upwards.