切る => Give up, stop... N3
Happens next
を[経「へ」]て => After A N1
Time, Situation
切る/切れる/切れない => to do something completely to the end/unable to do; too much to finish/complete N3
~をたて(~を経て)      => through; after; via N1
[切「き」]れない => Can't finish/complete A N3
Potential, Possibility
~をかわきりに(~を皮切りに)      => One after another; starting with ~ N1