No, you cannot split a proton into separate quarks, for multiple reasons: 

1) In quantum chromodynamics, Colour Confinements dictates that you can never have an isolated quark by itself that isn't bounded to anything. Since a proton is made up of three quarks, not matter how you split it, you will end up with a lone quark, which is impossible.

2) The force that bounds the quarks that makes up a proton is very strong, especially at a range as short as the gap between quarks. Overcoming that force is currently impossible with what science currently knows.

3) A proton is a kind of hadron. In a hadron, quarks are bounded by what's known as "gluon tubes". If you were to seperate a pair of quarks far enough for the gluon tubes to snaps, they will immediately from a quark-antiquark pair. But, in order to keep the net colour change zero, each particle in the pair will then be immediatelly attracted and bounded to the original pair of quarks anyway, thus bounding them back together again.
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