Short facing curve combined w/ a small tip opening makes this worse (relates to "surface tension" fluid dynamics)...you can use the suction approach as mentioned above (but I hate that, haven't done that since I was just starting out & playing in orchestral ensembles, plus if not careful, you can draw that stuff into your lungs & make yourself choke a bit, not good, hard to play well when you're choking/coughing!). But to get past it...put some steam behind your airstream...unless you're playing lots of classical/quiet "ppp" passages all the time, esp. in ensembles, give it some gas, step on it a little more, even though you may feel you're playing "too loud" at first. In the end, even if some wetness is in the mix, you'll literally blow the spit right out the other side...just drown it out w/ the wonderful sound of your horn, problem solved. Life is too short to play softly all the time...let it rip w/ a high velocity/efficient/focused powerful airstream (think firehose), get that reed vibrating like mad...the spit won't stand a chance

Here's a great example of drowning that sound out...in the first few phrases you may wonder how this guy could get a record deal w/ a "spitty" sound like that...but listen further into the tune as he "warms up the engine"...pushes more...I really think he wanted this to be a contrast in this tune, to capture the beauty of acoustic sax (he's a bit older, & I don't think he gives a damn about what people think, lol):