The method given below is based on the fact  that the two metal citrates differ largely in their solubility in the aqueous medium[ Cal citrate = 0.085 g/100 mL (18 °C);0.095 g/100 mL (25 °C) and  Mag. Citrate= 20g/100 mL—Wikipedia]

 So go on adding Ca(OH)2[  CaO, the lime]  maintaining   pH=7.2 at 70C.  Due to the  COMMON ION EFFECT(Cal Citrate is very less soluble  and  a  citric acid  is a week electrolyte with pK1,2,3=  3.09.4.75,5.41) and following the law of equivalents , it will precipitate as calcium citrate trihydrate and is filterd as filter cake of the rotatoty  vacuum filter while Mag.  Citrate will remain in solution.

Ref:

Biochemical Engineering and Biotechnology

 By Ghasem Najafpour

You may add hydrated lime, Ca(OH)2, to the aq. solution/suspension of magnesium and calcium citrate to favour the precipitation of calcium citrate while keeping the relatively more soluble magnesium citrate dissolved. After filtration, the magnesium citrate containing aqueous solution can be found slightly alkalinized by the added hydroxide, but can be neutralized with citric acid. The magnesium citrate can be recovered from the filtrate by evaporation and crystallization. The retained calcium citrate may contain excess lime, which can be then converted to calcium citrate, accordingly: 3Ca(OH)2 (s) + 2C6H8O7 (aq) → Ca3(C6H5O7)2 (s) + 6H2O (l). 

 The method given below is based on the fact  that the two metal citrates differ largely in their solubility in the aqueous medium[ Cal citrate = 0.085 g/100 mL (18 °C);0.095 g/100 mL (25 °C) and  Mag. Citrate= 20g/100 mL—Wikipedia]

 So go on adding Ca(OH)2[  CaO, the lime]  maintaining   pH=7.2 at 70C.  Due to the  COMMON ION EFFECT(Cal Citrate is very less soluble  and  a  citric acid  is a week electrolyte with pK1,2,3=  3.09.4.75,5.41) and following the law of equivalents , it will precipitate as calcium citrate trihydrate and is filterd as filter cake of the rotatoty  vacuum filter while Mag.  Citrate will remain in solution.

Ref:

Biochemical Engineering and Biotechnology

 By Ghasem Najafpour

Sorry both Manohar Sehgal and Carlos Araújo Queiroz don't care about the solublity product of ca(OH)2, which is less soluble in water. Instead of Ca(OH)2, you can try with CaCl2. In that you can achieve the above two statement may work.

 My submission is:

Will the presence of CaCl2  make  the  mixture solution slightly alkaline [ pH=7.2] or  acidic[ pH less than 7]?

DearManohar Sehgale 

Our goal to maximize the ionic strength of Ca2+. Hence the calcium citratre will precipitate out slowly from dissolved solution. The why we are worrying about pH for this context.

Citric acid is mainly produced via fermentation. A common procedure to recover citric acid from the fermenter's broth is that of precipitating calcium citrate with milk of lime. The precipitated calcium citrate is then treated with sulphuric acid, what causes the precipitation of calcium sulphate, while the citric acid is regenerated and solubilized. The filtrate is then evaporated and crystallized for the recovery of purified citric acid. The precipitation of calcium citrate with milk of lime is a somewhat complex process which can (possibly) be understood as involving the following equilibria: (i) Ca(OH)2 ↔ Ca++ + 2OH-, (ii) Ca++ + Cit--- ↔ CaCit-, (iii) CaCit- + Ca++ ↔ Ca2Cit+, (iv) Ca2Cit+ + CaCit- ↔ Ca3Cit2 , (v) Ca2Cit+ + OH- ↔ Ca2CitOH, (vi) 2Ca2CitOH ↔ Ca3Cit2 + Ca(OH)2. The solubility of calcium citrate increases at acidic pH, where the chemical species CaHCit, HCit--, H2Cit-, H3Cit (i.e. citric acid), Ca2H2Cit2, and H3O+, may play a significant role.