Welcome
matar961 to the Yamaha Forum!
You didn't mention which model engine you have (I run a 25 yr old 90TLRP and a 30 yr old Honda BF100E and I guess we should include that in our Profile 'signature').
By "...start to cut off..." do you refer to a reduction in RPM?
Yamaha's have a "Self-Protection" reduction to 2,000-2,200 RPM that is triggered by an overheat sensed or low oil on Oil-Injected models. Other 'triggers' vary by engine models.
These should be accompanied by an indication in the form of a warning buzzer and indication in the digital Tach.
",,,have to turn it off for about 30 minute." Points to overheat.
Only problems I've ever had with my Yamaha were Overheat Warnings.
First was when it was only five years old, caused by a pinhole corrosion leak from top cylinder combustion chamber into inner head water chamber. Due to all the cool water flowing through head's outer water chamber, it did not "feel" hot at all... (Takeaway from that was "Never Ignore an OH Warning" even if it "Feels" cool to touch (or Laser Gun).
Second (recent) was due to a partial blockage where water exits block into upper chamber exhaust route. Fresh Water Rinse after use and (much later use of) "Salt Away" had cooling chamber clean up where Thermostat and Pressure Regulator were located.
It took a removal of the cylinder head to see this pile of residue (in clumps too large to pass) causing restriction and my decision to also remove exhaust cover opened a real 'can-of-worms' for me.
You can confirm your Warning Buzzer (with key-switch 'On') by grounding the pink lead from an overheat sensor/s (usually near top of a cylinder head/s) or applying 12 volts to buzzer itself, first method preferred.
You can confirm integrity of your overheat sensor/s with an OHM Meter and Candy Thermometer in a heating pan of water on your stove. No continuity between pink and black until temperature passes 190f or so (check your engine's Service Manual) and circuit should reopen again as it cools down past 150f. Check your Thermostat/s at same time for opening at 130f or so and minimum rise of valve to 3/16ths" or so
You need to have a Service Manual if you want to be involved with your engines health. A minimum would be the Seloc Manual and that would be available in your local Library, purchased on eBay or a local 'used-book' store (where all my 'former' engine/auto SM's went). Clymer's Book is also excellent and the Factory SM for your model should be 'the bible' (it's quoted in those user manuals). Of course SM's for the more recent models can be purchased on this site or your local Marine Supply or Marina/Yamaha Dealer.
Best of luck with the problem and have a Great Holiday,
Art