Tiller starts, runs for 2 minutes, then engine slowly sputters and dies. In checking the engine oil, discovered gasoline mixed in with oil. Why would this happen? Solutions?

Two cycle engines run on a mixture of gasoline and oil. Each engine type is designed to run on a specific gas-to-oil mix ratio.
IMPORTANT: Use only oil that is labeled for use in "Two-cycle" or "Two-stroke" engines. Home Depot and other stores now have "premixed fuel" of gas and 2 cycle oil.
To mix two-cycle fuel, start by putting correct amount of oil in gas can. Then slowly add correct amount of gasoline. Do not try to mix gas and oil directly in gas tank of equipment.

IMPORTANT: Do not use any fuel that is over 30 days old. Do not mix more fuel than you are likely to use in a month. Old fuel can gum carburetors and prevent starting. Always use fresh fuel.

The chart below shows correct amount of oil per gallon that each mixing ratio requires. Expect that yours will be between 32 gas to1 oil and 50 to 1. 32:1 and 50:1 are most popular.
Ratio GAS:OIL UNITED STATES OIL per 1 U.S. GALLON Gasoline
(128 oz.) *INTERNATIONAL OIL per 1 IMPERIAL GALLON Gasoline
(160 oz.) *INTERNATIONAL OIL per 1 LITER Gasoline
(metric) 32:1 4 oz. 5 oz. 31.25 mL 40:1 3.2 oz. 4 oz. 25 mL 50:1 2.6 oz. 3.2 oz. 20 mL

The first thing I would do would be to dump out all of the old gasoline mix from the tank and replace it with fresh gasoline mixed with the proper amount of 2-cycle oil.

Look on top of the machine.If there is an oil fill then no you do not use mixed fuel if yes it needs engine oil,30 wt.If there is no engine oil fill then you use mixed oil and gas,at a 50:1 ratio.

O and I are the international symbols for off and on. The O is the off position and the I is the on position. Put the switch in the I position. Make sure there is properly mixed fuel in the tank. Your Mantis probably uses fuel mixed 1 part 2cycle oil to 50 parts gasoline. Push the primer bulb a few times until you see fuel in the bulb. Position the choke lever to full choke, open the throttle completely and use short, quick pulls on the rope until the engine sputters. Reposition to choke to half and pull the rope again. The engine should start at this time. Let the engine run for a few seconds, then push the choke lever to off. Go to work in the garden.
Good luck!

Carburetor problem. Two stroke engines use oil mixed with gas. Old fuel or setting over the winter will cause varnish and sludge in the Carburetor. Start by buying a can of carburetor cleaner and mixing a new can of fuel.
1) Dump the old fuel and check replace it with new.
2) Remove the air cleaner.
3) Pump the prime bulb 3 or 4 times, set the choke, spray the insides of the carb with the cleaner and then try and start it . It should sputter and run for a few second but chances are it will take a few sprays to clean the jets

Most likely not the answer you are looking for but here is a shot:

Pick up a bottle of the Echo brand 2-cycle oil. It will say "Extended Life" on the labeling. This is meant to run in Echo products, but it is a very FINE and well engineered oil. Mix it according to label directions for 50:1 ratios. (2.6 Oz. to 1 Gal. Gasoline)

When mixed at this ratio it provides MORE than adequate engine protection for ALL 2-Cycle engines, including those that run in 40, and 30:1 ratios.

I mix one 2-cycle tank to label instructions on the Echo oil for 50:1. It handily runs in my Echo chainsaws, non-echo trimmer, Poulan Pro leaf blower, etc. They all run different ratios, but THRIVE on the Echo mix without as much oily residue and smoke to boot!

CAUTION: I do not know of ANY OTHER MAKE of 2-cycle oil that CAN DO THIS *SAFELY*.

Remember:

Always mix your 2-cycle fuel starting with *fresh* gas.

Mix only that which you can use in 30 days.

Use 89 Octane fuel to make your mix in small piston 2-cycle engines.

Clean and re-oil intake filters @ every 10 hrs. operation time. Check and re-gap your plug when you service your filter!

DRAIN unused fuel from tank back into gas mix container. Restart and let engine idle to run any remaining fuel out of engine and carb. Storing fuel in ANY 2-cycle longer than two weeks is going to gum them up and nothing short of a carb rebuild will get them sputtering back to life again!

FUELING ENGINE
WARNING: Remove fuel cap slowly
when refueling.
HELPFUL TIP
To obtain the correct oilmix
ratio, pour 3.2 ounces of
2--cycle synthetic oil into
one gallon of fresh gas.
This engine is certified to operate on unleaded
gasoline. Before operation, gasoline must be
mixed with a good quality synthetic 2-cycle
air-cooled engine oil designed to be mixed at a
ratio of 40:1. Poulan/Weed Eater brand
synthetic oil is recommended.Mix gasoline and
oil at a ratio of 40:1. A 40:1 ratio is obtained by
mixing 3.2 ounces (95ml) of oil with 1 gallon (4
liters) of unleaded gasoline. DO NOT USE
automotive oil or marine oil.

Hi a safe fuel mix is 25:1 but most homelites run a mix of 32:1 either one should be ok

That fuel/oil mix ratio should be 32to1 or 32 ounces gasoline to 1 ounce oil. You will have to make up a new mix and probably clean the fuel system and the spark plug before it will start.