I believe that it may be possible to shoot down a cruise missile with a shoulder-fired SAM, but in a real-world situation it's probably extremely unlikely.
Due to the average cruise missile's NOE flight profile, and reduced signatures, it's very difficult for major air defence networks to detect a cruise missile- let alone troops in the field.
A cruise missile usually flys low and relatively slow- but just fast enough to pass over a MANPADS crew, and disappear behind structures or terrain features before the crew can realistically acquire and lock onto the missile.
Typically, the small turbofan engines powering a modern cruise missile don't generate a large heat signature either, which makes a solid lock-on a difficult proposition for most MANPADS.
The best defense against low flying cruise missiles is not a foot soldier with a short-range SAM- it's a modern, over-lapping, multi-tiered, digitally networked air defense grid.
For this reason, it becomes quite obvious why cruise missiles are so highly prized as a first strike option. Combined with jamming, decoys, SPECOPS, stealthy aircraft, and a range of other options- the modern cruise missile is a very effective, low risk strike weapon.
Building such an effective, sophisticated, and elaborate defense network against them is cost prohibitive for most nations.