Chiefs QB Alex Smith is so desperate to put his 8 years in San Fran behind him ... he just slashed a cool $300K off the asking price on his CA mansion, TMZ Sports has learned.

Smith originally listed the 5,650 sq ft, Los Gatos home for $3.25 mil -- after getting traded to the Chiefs last year ... but now he's settling on $2.95 mil in a last ditch effort to unload the place.

The 4 bedroom, 4 bath crib includes a massive 1,200 sq ft master bedroom ... and sits on a shaded hilltop an hour south of soon-to-be demolished Candlestick Park.

Here's what's inside -- high vaulted ceilings, hardwood floors, and huge windows with amazing views. What's NOT inside? A Lombardi Trophy, cause y'know ...

Fun Fact: Our friends at Realtor.com tell us there are now two CA homes on the market owned by former No. 1 picks. Ex-Texans star David Carr is also trying to unload his Bakersfield mansion for $2.8 mil.