Miter Saw tripping breaker, but
This is an interesting situation and the problem you have could be for more than one reason. I am going to try and explain it without getting too deep into the science behind it.
First you have simply too many pieces of equipment attached to your circuit. Since I don't know specifically the name plate ratings of you refrigerators or the freezer I have to use generic amperage's. A standard 20-25 cu/ft refrigerator uses 3.5 - 4 amps when it is running and a 10 cu/ft freezer uses about 2.5 amps. Your 15 amp miter saw will run about 1700 watts or 14 amps under full load. So if you add this altogether 3.5+3.5+2.5+14 it comes out to 23.5 amps.
Logically speaking you should be asking why doesn't it trip all the time? Well to start refrigerators and freezers only run about two hours a day, and your Miter saw pulls 14 amps if it is under full load. If you are cutting smaller softer wood then there is a good chance your Miter saw is only running at about half of full load or more like 7 amps. So when a any of these appliances are coming on there is a start up surge and if any other equipment is running it may be enough to trip a breaker.
That explains why you are tripping a breaker, but why doesn't it trip if you put the miter saw on a 100' extension cord?
That would have to do with voltage drop, demand amperage and fault current. Very basically it means that when you add a 100' of extension cord you get a situation where when your miter saw starts and it calls for 14 amps, the length of the circuit creates so much voltage drop it can't deliver 14 amps. Instead it is delivering say 10 amps. This causes the motor and the circuit conductors to heat up causing more resistance causing less amperage to be delivered to the load. So there is not enough energy being passed through the circuit to cause an overcurrent situation which means the breaker wouldn't trip. This could also be true of the old circuit if there were corrosion or loose connections causing more resistance in the line.
Even though it appears that adding an extension cord fixes the problem it really doesn't. Compressors and motors don't like low voltage situations. They heat up and overwork and eventually burn up. That is why major appliance manufacturers specifically state not to use extension cords, otherwise it will void their warranty.
As I stated earlier I don't have specific information about your situation so I can't make a definitive conclusion, but based on generic information and the situation you have given, this would be my best guess as to what is happening.
I would suggest you investigate this particular circuit and check it for loose fittings and corrosive wiring and verify correct wire sizes. I would also suggest you add a few circuits to distribute the load a little better.
Hope this helps and good luck.