government ministry, conserve, omit
省 centers on reducing or streamlining: conserving resources, omitting unnecessary parts, or a government ministry that oversees efficient administration.
省 combines 少 (few, little) with 目 (eye), suggesting inspecting with a discerning eye to reduce or omit. The government ministry sense likely developed from the idea of oversight and streamlining.
With a sharp eye (目) you spot what is few (少) or unnecessary, so you conserve and omit. A government ministry does the same: it oversees and cuts waste.
For セイ, imagine a ministry official saying 'Save it!' (セイ) while cutting a budget: 'Say' -> セイ, and the eye (目) spots the savings.
reflection; reconsideration; introspection; meditation; contemplation
omission; leaving out
Ministry of Labour (now Ministry of Health, Labour and Welfare)
Ministry of Foreign Affairs
homecoming; returning home
ministries and government offices; the authorities
to omit; to leave out; to exclude; to eliminate
Ministry of Justice
Department of State (US); State Department
ministerial ordinance
the said ministry; the same ministry
to reflect on (oneself, past conduct, etc.); to contemplate; to examine; to think over; to introspect
(former) Ministry of Health and Welfare
introspection; reflection on one's self
Ministry of Education, Science and Culture (1871-2001)
energy conservation; economical use of energy; energy-saving
Ministry of Finance (1869-2001)
labor saving; reduction of labor
Ministry of Transport
self-examination; reflection
ministry proper; home office; head office
Ministry of International Trade and Industry (1949-2001); MITI
Ministry of Construction
frequent reflection; frequent meditation