Today's border slash (more commonly known as a border vista) was made in the early 1900's in order to carry out the requirements of the Treaty of 1908 and the Treaty of 1925. These treaties called for an effective and plain demarcation of the border, in order to easily settle any conflicts that may arise from poor surveying or unclear markers.
The Treaty of 1908, which led to the creation of the International Boundary Commission, states the following in Article VI regarding how the border should be marked:
... and boundary marks shall be established wherever necessary, in the judgment of the Commissioners, to meet the requirements of modem conditions and to render more effective the demarcation of the existent boundary established under the Treaty provisions...
And this is expanded by Article IV of the Treaty of 1925, referring to the work done to mark the border since the Treaty of 1908:
And whereas boundary monuments deteriorate and at times are destroyed or
damaged; and boundary vistas become closed by the growth of timber;
And whereas changing conditions require from time to time that the boundary be marked more precisely and plainly by the establishment of additional monuments or the relocation of existing monuments;
The Contracting Parties, in order to provide for the maintenance of an effective boundary line between the Dominion of Canada and the United States and between the Dominion of Canada and Alaska, as established or to be established, and for the determination of the location of any point thereof, which may become necessary in the settlement of any question that may arise between the two Governments...
A joint report by the American and Canadian boundary commissions in 1925 describes how the above treaty provisions have already been implemented, and how they should be maintained. In particular, the 3 meter/20 foot wide border vista was defined:
VII. That the boundary through timbered areas should be further marked by
a vista of sufficient width to give a cleared 20-foot sky line along the boundary
In short, Canada and the US agreed that the border should be clearly marked, probably to prevent the sort of conflicts and disputes that happened in the past due to unclear borders. Having a giant line chopped through a forest certainly meets the treaty requirements of a clear demarcation, and helps stop the common person from accidentally settling in another country.