1.
If you chip away at something such as an idea, a feeling, or a system, you gradually make it weaker or less likely to succeed by repeated efforts.
Instead of an outright coup attempt, the rebels want to chip away at her authority.
= erode
PHRASAL VERB : V P P n
2.
If you chip away at a debt or an amount of money, you gradually reduce it.
The group had hoped to chip away at its debts by selling assets.
PHRASAL VERB : V P P n