rooting up; pulling up by the roots
Literal sense of physically uprooting plants, weeds, etc.
I pull up the weeds in the garden by the roots.
eradication; stamping out; rooting out
Figurative sense of completely eliminating something undesirable, such as a problem, crime, or bad habit.
The government aims to stamp out corruption.
Compound of 根 (ne, 'root') + 絶やし (tayasi, the continuative form of 絶やす (tayasu, 'to exterminate, to let die out')). The reading ねだやし shows rendaku (voicing of た to だ).