We decided to review the budget and cut costs.

Literal

Budget [object-を] examine-[continuative-し], cost [object-を] reduce-nominal [decide-ことにした].

Two conjunction points: the stem-form 検討し (the ~し continuative) links the first clause without a te-form; and ~ことにする ('decide to') is the standard way to express a personal decision. 検討する ('to examine, deliberate, review') is a common business verb for studying a matter carefully before acting. 削減 ('reduction, cutback') is formal vocabulary for budget or staff cuts.