No, you cannot.
The IRS allows to claim a dependent only once. If you do claim the grandchild and his mother has already done so, your return will be rejected.
If you believe that you qualify -and not your daughter - to claim the child, you would have to mail your tax return with proof showing why you are entitled to claim the grandchild (school records, medical, support). It would take a long time for the IRS to process your return. They literally look at the proof and decide who should claim the child.