As I recall, from Vice City onward saving the game in a safe house removes the wanted level entirely in the Grand Theft Auto series. However, in GTA III this doesn't appear to have any effect.
Getting rid of the wanted "stars" is very time-consuming as the police seems to follow you to every corner of the map at +★★. The full in-game map hasn't been introduced yet in the series and Pay 'n' Spray stations aren't highlighted on the minimap, leaving searching for police bribes (reduces the wanted level by one) as the last option.
The Grand Theft Auto wiki page for Grand Theft Auto III lists various ways on how to reduce wanted levels, including the state of using safehouses.
One of them is indeed using the save point, however this is from GTA Vice City and onwards.