This is the 17322nd most frequent Russian word.
сэкономив
"Having saved" or "by saving."
The word 'сэкономив' is used in the participial form as an action modifier indicating the method by which the subject achieved the main goal of the sentence.
Сэкономив деньги, мы смогли позволить себе поездку.
By saving money, we were able to afford a trip.
Here 'сэкономив' describes the means by which the subsequent action (buying a book) was made possible, focusing on the method of saving.
Она купила книгу, сэкономив на обедах.
She bought a book by saving money on lunches.
The participial usage of 'сэкономив' reflects the reason or method leading to the completion of the primary action (finishing the project early).