The LM6181 is not a typical op amp. It operates in a current feedback mode, not a voltage feedback mode. It's advantage is that is generally has a higher frequency response than the usual voltage feedback op amp. But it may not operate properly in some of the typical op amp circuit configurations.
That being said, it should work OK if you use it as an inverting summing amp. (You tried to connect it up as a non-inverting amp which is not a true summer) For this connect the positive (non-inverting) input to ground and leave the 820Ω feed back resistor from the output to the minus (inverting) input. Then add two 820Ω resistors, also to the minus input. Connect the input signals to each of these resistors. That will give you a summing amp with a gain of -1 for each input.
(Note that summing a ±5V triangle wave with 0-1V sine wave of the same frequency will just give a distorted appearing triangle wave, the shape depending upon the phase between the triangle wave and the sine wave.)
You aren't trying to build a modulator are you, where you want the product of the two waveforms, not the sum?