A method for removing an undesirable material is provided. The method includes maneuvering a first cannula within a vessel such that it is positioned for capturing the undesirable material. The method also includes positioning a second cannula within the vessel such that it is in a spaced relation to the first cannula. A suction force may be provided so as to capture the undesirable material through the first cannula. The undesirable material may be fragmenting as it is drawn along the first cannula, so as to enhance removal of the undesirable material through the first cannula. A system for removing an undesirable material is also provided.