Have shot quite a few Speer handgun bullets, but I don't recall ever loading/using those.
Speer's website calls it a "target" bullet. But, deer aren't hard to kill. You've got 240 grains of metal there, coming out of a 44 mag. It ought to make a hole.
Speer makes a .458 300 grain they also call a Plinker. But loaded up in a .45-70 or .450 Marlin it is a great bullet that holds together extremely well and seems to perform as good or better than bullets that are marketed as a hunting bullet. If their 44 Plinker is built the same way I’d say you’ll no problems whatsoever with it.