Referring particularly to the solemn injunction which he had just given him, to "fight the good fight of faith," but perhaps also including all that he had enjoined on him. –Barnes

Two things are mentioned here:

1. That the commandment itself-the whole doctrine of Christ, should be kept entire.

2. That his life should be agreeable to that doctrine. Keep it without spot-let there be no blot on the sacred book; add nothing to it; take nothing from it; change nothing in it. Deliver down to thy successors the truth as thou hast had it from God himself. –Adam Clarke

That thou keep this commandment. Commandment seems to be used here as a comprehensive word for the Gospel, as Christ used it in John 12:50 –Wycliffe 

And I know that his commandment is life everlasting: whatsoever I speak therefore, even as the Father said unto me, so I speak. –John 12:50

Keep this commandment-Greek, 'the commandment;' i.e., the Gospel rule (John 13:34; 1 Tim 1:5; Titus 2:12; 2 Peter 2:21; 3:2). –JFB

A new commandment I give unto you, That ye love one another; as I have loved you, that ye also love one another. –John 13:34

Now the end of the commandment is charity out of a pure heart, and of a good conscience, and of faith unfeigned. –1 Tim 1:5

Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world. –Titus 2:12

For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them. –2 Peter 2:21

That ye may be mindful of the words which were spoken before by the holy prophets, and of the commandment of us the apostles of the Lord and Saviour. –2 Peter 3:2

It is clear that "this commandment" is in reference to the entire gospel rule.  This is how the church is taught today.  It is taught doctrine which is the whole Word of God and Christ in particular.
 

It seems harsh, and is unusual, to apply the epithet, "without spot"-aspilos (NT:784)-to a command or doctrine, and the passage may be so construed that this may be understood as referring to Timothy himself-"That thou keep the commandment so that thou mayest be without spot and unrebukeable.  The word here rendered "without spot," occurs in the New Testament only here and in James 1:27; 1 Peter 1:19; 2 Peter 3:14. It means without any "stain" or "blemish; pure." If applied here to Timothy, it means that he should so keep the command that there would be no stain on his moral character; if to the doctrine, that that should be kept pure.

Pure religion and undefiled before God and the Father is this, To visit the fatherless and widows in their affliction, and to keep himself unspotted from the world. –James 1:27

But with the precious blood of Christ, as of a lamb without blemish and without spot. –1 Peter 1:19

Wherefore, beloved, seeing that ye look for such things, be diligent that ye may be found of him in peace, without spot, and blameless. –2 Pet 3:14 --Barnes

Keeping the commandment spotless and without reproach means both teaching and living above reproach. –Wycliffe