Good news/bad news.  While it is "easier to break frozen tissue into halves compared with intact tisssue, freezing tissue has some consequences. Frozen section cut on a cryostat and post fixed after sectioning is never as good as tissue that is first fixed. If you are performing biochemical analyses, then you may have little choice but must recognize that tissue frozen, then thawed for fixation will lose some antigenicity and will certainly reduce morphology. It really depends on what the "other analyses" are.  If mRNA, fixation can be good and I'd recommend embedding tissue in egg yolk gelatin, postfixing it in formaldehyde for a few days then you can cryoprotect the block in sucrose, freeze and cut on a cryostat.  Freely floating sections that retain both mRNA and protein are then possible if in situ hybridization is your goal for the other analyses. Quantitative in situ with biotinylated probes and ABC detection of the biotin (anti-biotin being the first step, biotinylated secondary, then ABC, as in:

Berghorn, K.A., Le, W.W., Sherman, T.G. and Hoffman, G.E. The suckling stimulus suppresses messenger RNA for tyrosine hydroxylase in arcuate neurons during lactation. J. Comp. Neurol: 438: 423-432, 2001. PMID: 11559898 and

Hoffman, GE, Le, WW, Entezam, A, Noriyuki, O., Tong, Z-B, Nelson, L, Flaws, JA, McDonald, JH, Jafar, S., and Usdin, K. Ovarian abnormalities in a mouse model of Fragile X primary ovarian insufficiency. J. Histochem. Cytochem, 60(6): 439-456, 2012, ePub April 2 doi:10.1369/0022155412441002. (has embedding component for mouse ovaries)

Good news/bad news.  While it is "easier to break frozen tissue into halves compared with intact tisssue, freezing tissue has some consequences. Frozen section cut on a cryostat and post fixed after sectioning is never as good as tissue that is first fixed. If you are performing biochemical analyses, then you may have little choice but must recognize that tissue frozen, then thawed for fixation will lose some antigenicity and will certainly reduce morphology. It really depends on what the "other analyses" are.  If mRNA, fixation can be good and I'd recommend embedding tissue in egg yolk gelatin, postfixing it in formaldehyde for a few days then you can cryoprotect the block in sucrose, freeze and cut on a cryostat.  Freely floating sections that retain both mRNA and protein are then possible if in situ hybridization is your goal for the other analyses. Quantitative in situ with biotinylated probes and ABC detection of the biotin (anti-biotin being the first step, biotinylated secondary, then ABC, as in:

Berghorn, K.A., Le, W.W., Sherman, T.G. and Hoffman, G.E. The suckling stimulus suppresses messenger RNA for tyrosine hydroxylase in arcuate neurons during lactation. J. Comp. Neurol: 438: 423-432, 2001. PMID: 11559898 and

Hoffman, GE, Le, WW, Entezam, A, Noriyuki, O., Tong, Z-B, Nelson, L, Flaws, JA, McDonald, JH, Jafar, S., and Usdin, K. Ovarian abnormalities in a mouse model of Fragile X primary ovarian insufficiency. J. Histochem. Cytochem, 60(6): 439-456, 2012, ePub April 2 doi:10.1369/0022155412441002. (has embedding component for mouse ovaries)

Besides Gloria's tipps and reference to special literature it might be asked (and I would like to ask you): i) first of all: is it a secret what you will be dividing?

ii) why thinking about freezing (with all its consequences, see above) and then "breaking"?? I am sure you never get it into 2 nearly mirroring real "halves" (also consider "breaking = fracturing"  along internal tissue structures....

iii) my personal and honest recommandation (if it is not bone or really hard concrement you have to prepare for histological examination):

1) use dissecting stereoscope,

2) buy really high-quality razor blades (like Gilette Silver) 

3) degrease each of the razor blades carefully & cautiously (CAVE: new - and old -  razor blades can harm you / at least your fingers seriously if you do it incorrectly (:-)), the old ones can be infectious.... (for degreasing use either 96-100% alcohol or 100% acetone and lintfree kitchentowel)

4) under stereomicroscopical observation and immersed in a big drop of fixative  [NB:  or - if considering freezing the second part - in buffer solution (e. g. physiological PO4-buffer pH7.4, ~ 300 mosmol)]  carefully divide your specimen exactly in 2 parts

(considering the right section plane, use specific / suited - non sucking and inert plastic / teflon  cutting mat) [transfer / change the second part from buffer to fixative of your choice]  

and proceed with both specimen halves as you have to....

Best wishes, good luck,  regards, WM.

Hello,

If the tissue is the brain, you can prepare artificial CSF and put inside until you are ready to use or fix in formalin

Without oxygen, however the tissue will not be stable for too long. I agree with Wolfgang's recommendation

I will suggest you fix your brain sample in required (literature proveen) fixative of choice. Though the choice of fixative depends on what you are studying in the brain.

You could freeze and embed the tissue specimen in OTC block, thereby avoiding a need for embedding it in paraffin block. Subsequently, you could section the specimen directly from the OCT block.