Inside the AD5541A, the MOSI bits get clocked into a shift register and are held there until the ~CS line goes high. At that time, the bits are transferred from the shift register to the D/A. It does not matter what level is on MOSI at that instant.
In the traces I posted earlier, I included a transition from full scale output to 0. I also show several cycles of writing all possible values in a ramp. The resulting voltage waveform shows the AD5541A is seeing the data correctly. The last four writes to the pmod in the zoomed trace show sending the values 0, 1, 2 and 3 to the D/A. You can observe SCLK's transition in relation to the least significant bits of the data. SCLK is not transitioning when ~CS transitions to high so the data on MOSI is "don't care" at that instant.
I did use different clocks since the microblaze can run at higher clock rates than the AD5541A. Also, when you are troubleshooting, it can sometimes help to slow down the logic.
I see you are using pmod connector JB whereas my project used JA. Just as a test, you might want to try moving your PmodDA3 to JA and use my project as is to replicate my results.
You should be able to launch vivado, open my project then immediately launch the SDK from vivado. You should not have to generate a bitfile. I had included the hardware handoff in the zip file I gave you so you have my exact bitfile. Once the SDK loads, it should automatically load the project and compile it. At that point you can program the fpga from inside the SDK and then run my example app. You should see a sawtooth waveform coming out of the PmodDA3 if all is well.