If approved, the cuts, totalling £12.8m for 2015/16, will see a rise in council tax, day care centres closing and street cleaning reduced.
The move comes after the Welsh government's recent budget included a 3.4% cut in funding for the council.
Further cuts of over £14m in 2016/17 and £12m in 2017/18, are also planned.
Despite the endorsement by the cabinet, council leader Keith Reynolds said the proposals were still subject to further consultation over the coming months.
He said: "I am confident that with everyone's full support, we can ensure a balanced, fair budget with the best interests of the people of our county borough."
Mr Reynolds was keen to stress the council wanted to avoid staff redundancies wherever possible.
He said: "These are undoubtedly unprecedented financial times for councils across Wales.
"But I want to give a very strong message that it is our overwhelming intention to protect front line services where we possibly can."
Other savings proposals include the removal of Bargoed's annual ice rink, a rise in the price of meals on wheels and limited library opening times.
Turning off of street lights at certain times and removing funding to help pensioners pay council tax are also recommended.
The 3.9% council tax increase will, if approved, result in a weekly increase of 48p for Band A properties and 71p for Band D properties.
Mr Reynolds added: "The savings targets facing us are undoubtedly tough, and we will need to take some difficult decisions.
"But I am confident we will continue to deal with these challenges with a measured and balanced approach."
The cuts, which will total savings of £39m over three years, will now be scrutinised before the council votes on them in full in February.
Services are to be hit significantly after draft savings and budget cuts were endorsed by Caerphilly council's cabinet.