Actually it's your opinion that the word does not mean what it means because you do not want it to mean what it means. The word "determined" in Daniel 9:24 means the same thing as "490 years have been decreed by God". The word 'achar (after) in verse 26 means that God determined that the Messiah would be cut off in the 70th week, and we know that it was in the midst of the 70th week that He was cut off:
"And I will establish my covenant [H03772 karath] with you; neither shall all flesh be cut off any more by the waters of a flood; neither shall there any more be a flood to destroy the earth.
[H3772 karath]
to cut (off, down or asunder); by implication, to destroy or consume; specifically, to covenant (i.e. make an alliance or bargain, originally by cutting flesh and passing between the pieces):--be chewed, be con-(feder-)ate, covenant, cut (down, off), destroy, fail, feller, be freed, hew (down), make a league ((covenant)), X lose, perish, X utterly, X want.
"And after [H0310 'achar] threescore and two weeks shall Messiah be cut off [H03772 karath], but not for himself: and the people of the prince that shall come shall destroy the city and the sanctuary; and the end thereof shall be with a flood, and unto the end of the war desolations are determined. (Daniel 9:26)
There's the covenant mentioned right there - in Daniel 9:26 - by the word translated as "cut off". It's saying that Messiah shall cut a covenant after the first 483 years:
And he shall confirm [H01396 gabar] the covenant with many for one week: and in the midst of the week he shall cause the sacrifice and the oblation to cease, and for the overspreading of abominations he shall make it desolate, even until the consummation, and that determined shall be poured upon the desolate. (Daniel 9:27)
[H01396 gabar gaw-bar']
a primitive root; to be strong; by implication, to prevail, act insolently:--exceed, confirm, be great, be mighty, prevail, put to more (strength), strengthen, be stronger, be valiant.
This is talking about His life:
"He was taken from prison and from judgment: and who shall declare his generation? for he was cut off [1504 gazar] out of the land of the living: for the transgression of my people was he stricken." (Isaiah 53:8)
This is talking about the covenant He cut in His blood:
"And after [H0310 'achar] threescore and two weeks shall Messiah be cut off [H03772 karath], but not for himself: and the people of the prince that shall come shall destroy the city and the sanctuary; and the end thereof shall be with a flood, and unto the end of the war desolations are determined. (Daniel 9:26)