I am sorry you and your daughter are going through this. It sounds like you and your ex are on completely different planes about this - perhaps that's one of the reasons he's your ex.
I don't know if this dilemma is due to cultural differences, personality differences, philosophical differences, or some combination. Or perhaps some desire to control you through controlling your child. Was he abusive and controlling when you were together? But it's abusive. He's blaming you for "the situation."
As this country is starting to come to grips with the folly of its obsession with standardized testing and as more and more schools, colleges and parents are opting out, it's a shame he is clinging to a particular viewpoint.
I'm sorry he views math and science as being supreme in "this age" and I'm sorry he thinks she needs those things to be an artist, or a social worker, or a music teacher. Or happy. Memorizing is ridiculous. Six-year-olds should NOT be memorizing multiplication tables at all, and they should not be doing homework at this level when assigned by a parent. Or by a teacher, for that matter. I disagree vehemently with the response below that says she must be enrolled in Kumon or something else. She doesn't need to be. In fact, unless she has a burning desire, she shouldn't be.
There are all kinds of learning. Kids learn through play, through reading, through visits to museums, through social activities, through art and music and dance...He's so wrong if he thinks he is "making her smart" - he is making her stressed, making her regimented, making her a regurgitation machine spewing facts. That is so far from "smart" that it's ridiculous. I'm sorry he has such a narrow view of intelligence. So I suggest you ignore his dictates to provide her with worksheets, and you protect your time with her. He may continue to torture her and, as she grows older, she will resent him and not wish to spend time with him. I think you should alert her teacher and hopefully get him to attend the school parent-teacher conference so the teacher/staff see what this child is up against. Let them explain the many types of assessments available, and how standardized testing of facts and recitation of times tables misses 90% of her abilities.
If you see signs of anxiety in her (sleep problems, eating problems, any negative habits or self-harm), consult her pediatrician immediately.
I'd work with the school psychologist on wording your daughter might use if the "my mom says..." triggers him. (Which, by the way, tells me it's about his anger toward you in general and not about her and her education.) But he's got to learn, perhaps through family counseling, that shutting her down is highly negative and very damaging.
I'm not sure you can educate him - he seems to have his own view of "education" and your views aren't included. You may have to limit her time with him but you'll have to go through the legal system to do that.
Start with the schools, her doctor (and maybe an outside counselor), and your lawyer, I think. Maybe he just needs some help and assurances regarding the public education process in this country, and some awakening about experiences he may have had as a child (which perhaps damaged him and made him so angry and so concerned about inadequacies?) - perhaps he will consider not doing to his child what was done to him.