It can be done.
Assume that you take some 20 microL of blood, you would need a detection limit for your HPLC method of under 1 nmole of amino acids injected on column. With the AccQ-Tag derivatization, you can get down to 50 pmoles on column, so it is possible to do this without your mice dying on you.
I have a good idea about a solid sample preparation protocol, but you need to do some homework with standards to work out the details of the method. The idea is to use a combination of cation exchange, anion exchange and hydrophobic interaction to get rid of the majority of the interferences in sample preparation. We have done work like this for drugs with a dual charge, just like your amino acids.
You will need to work out the protocol with some Oasis SPE cartridges and standards, and then probably transfer the protocol for your mouse samples to a 96-well microElution plate. You will need to see at the end, what sensitivity your LC method will give you.
The protocol will use an Oasis MCX cartridge, and an Oasis MAX cartridge. The first one is a hydrophobic strong cation exchanger, the second one is a hydrophobic strong anion exchanger. We will work out the protocol first with standards, so you will make a solution of your amino acids at the intended concentration levels. You will treat the mouse plasma sample later in the same way. You take an aliquot of your amino acid solution, add an internal standard of similar properties as your analytes, i.e. something like gamma-aminobutyric. You acidify the sample to pH 1 with HCl. This sample is loaded onto the Oasis MCX cartridge (you can look up details of the protocol on the Waters website). The analytes will stick via ion-exchange. You wash the adsorbed sample with (acidified?) water. Then you elute at an alkaline pH, either with 2% ammonia or NaOH. I prefer the first option. If all your amino acid elute quantitatively, you are fine. If they don’t you may need to add 10% or 20% of methanol to the elution solvent. If this is indeed needed, you should use the same amount of methanol in your wash solvent (the step before the elution step) as well.
Now you have this alkaline solution of the amino acids. You add them to the Oasis MAX cartridge (after activation of the cartridge). Your amino acids will now be retained by anion exchange. You wash with water (maybe with some base added?) and elute under acidic conditions, probably again with HCl. As above for the cation exchange, you may need to add some methanol, if the elution is incomplete, and you would add the same concentration of methanol in the wash protocol.
Here is what is happening: you load the amino acids onto the MCX cartridge. You wash out sugars and other neutral polar compounds with the first water wash step together with all polar anions that do not stick to the packing. Also, most of the proteins and other large molecular weight compounds will wash out, because they do not get into the pores of the packing. You are left with cations and neutral hydrophobic compounds on the surface. You now elute your amino acids with a polar alkaline solvent. Only polar compounds that had been positively charged will elute, and hydrophobic compounds will be left behind. In the next step, you now adsorb all negatively charged compounds onto the MAX cartridge. Only zwitterionic compounds from the first step will stick, while straight amines will wash through the anion exchanger. If there has been an issue of some carry-over of hydrophobic compounds, they will stick, too, but you will leave them on the cartridge with the selective elution of the amino acids at low pH.
Sounds complicated, but it really is very simple from the standpoint of execution.
Have fun!