Dave Stevens is the guy to ask.
i do everything with a band saw i do not use a table saw for anything
but
if the saw cuts all along the board the way you show, it is a blade problem. the teeth on the blade are wacked out of alignment. Some woodworkers bend a few teeth to get that rustic saw cut look.
if it happens only when you start a cut it is the saw. But to make sure try cutting again with something thicker like a 3 x 3 to make sure there is no wiggle in holding the board against the fence and on the table.
things i would try
1 take a board the wider than the height of the cut and set the fence so you are just taking a surface cut . Feed the board in very slow and keep an eye on the blade see if it moves or you feel it is starting to bind.
theory here is like riding a motorcycle as long as the wheels are turning the bike will stand up right. As long as the blade is spinning it will stay true once you apply a force the blade moves.
so is the blade tight on the arbor?
is the arbor running ture?
i would rule out the power source because that would cause the cut to continue all along the board and not just at the start.
then the idea that tools do wear out and parts get loose. but that would cause the cut to continue along the board and not just at the start.
a tune up
with a band saw all tuned up and adjusted you can resaw a 6 x6 x 4 foot beam to within .020 thousandths the entire length and width.
the table saw may need a tuneup.
use a square on the table and against the blade, give the blade a slow spin and see if it is running square to the table.
is the fence parallel to the blade?
operator error if the width of the board is wider than the height of the fence when you first feed the board into the saw the board pivots at the top of the fence ever so slightly and kicks out at the table level. It is so slight you don't even feel it move.
and that was a bunch of randon thoughts