The spindle occupies a central position in cell division as it builds up the chromosome-separating machine. Here we analysed the dynamics of spindle formation in acentrosomal plant cells by visualizing microtubules labelled with GFP-EB1, GFP-MAP4 and GFP-α-tubulin and chromosomes marked by the vital dye SYTO82. During prophase, few microtubules penetrate the nuclear area, followed by nuclear envelope disintegration. During prometaphase, microtubules invading the nuclear space develop a spindle axis from few bipolar microtubule bundles, which is followed by spindle assembly. Using a novel quantitative kymograph analysis based on Fourier transformation, we measured the microtubule growth trajectories of the entire dynamic metaphase spindle. Microtubules initiating from spindle poles either pass through the metaphase plate to form interpolar microtubule bundles or grow until they reach chromosomes. We also noticed a minor fraction of microtubules growing away from the chromosomes. Microtubules grow at 10 μm/minute both at the spindle equator and at the spindle poles. Photobleached marks created on metaphase and anaphase spindles revealed a poleward tubulin flux. During anaphase, the velocity of tubulin flux (2 μm/minute) equals the speed of chromatid-separation. With these findings we identified spatially coordinated microtubule growth dynamics and microtubule flux-based chromosome-separation as important facets of plant spindle operation.