|I have large, yellow worms on my mandevilla. They have several appendages, like antennas.|
|This sounds like a caterpillar. You may be about to have a butterfly show at your place! Some species of caterpillar will extend antennae-like structures when disturbed. The simplest control is to hand pick and destroy them, although I'd suggest you leave a few to see how they turn out.
Another safe control options is the use of a product containing B.T., a biological spray for caterpillars. Sprayed on the plant foliage, B.T. will make the caterpillar sick when it eats the sprayed foliage. Affected caterpillars soon stop feeding and die. Beneficial insects are not affected.