Our Gemara on Amud Beis references the concept of Mitzvos Lav Leyhanos Nitnu.  That is, the observance of a Mitzvah is not based on experiencing any pleasure.  Thus, in theory if one made a vow to not receive any benefit from an object, in certain circumstances, he may still utilize it in the performance of a mitzvah. If a person vowed not to receive benefit from a shofar, he can still use it to blow on Rosh Hashanah, as the mitzvah is not designed nor is experienced as a physical pleasure.  On the other hand, if he played the shofar as a musical instrument, enjoying the notes and tunes would be forbidden.  (If a mitzvah also brings physical pleasure, it still may be forbidden, such as a person who vowed to abstain from a mikvah and then immerses for mitzvah purposes.  If it is a hot day and he also cools off from the water, this may be forbidden even when doing the mitzvah of tevila. See Ran Nedarim 15b)

This needs some clarification as it is indeed proper to enjoy mitzvos.  The verse states (Devarim 28:47):  

תַּ֗חַת אֲשֶׁ֤ר לֹא־עָבַ֙דְתָּ֙ אֶת ה אֱלֹק֙יךָ בְּשִׂמְחָ֖ה וּבְט֣וּב לֵבָ֑ב מֵרֹ֖ב כֹּֽל

Because you would not serve your Hashem, your God, in joy and gladness over the abundance of everything.

(See Ohr Hachayyim and Rabbenu Bechaye Op. Cit.)

And, of course, Tehillim (100:2):

עִבְד֣וּ אֶת־ה בְּשִׂמְחָ֑ה בֹּ֥אוּ לְ֝פָנָ֗יו בִּרְנָנָֽה

worship the LORD in gladness; come into His presence with shouts of joy.

(See Chomas Anach Op. Cit.)

The Derashos of the Chasam Sofer (Nitzavim 115) explains that the mitzvos are experienced on two levels. The majority of people are only capable of performing the mitzvos as commandments. In such a manner, it is not a pleasure but a duty. There is also another dimension which is a sublime spiritual pleasure at becoming attached to Hashem through emulation and harmony with His will wisdom. This enjoyment is quite real and intense. Even so, it is not a violation of the oath because the pleasure is not from anything physical that is occurring or located within the object. So we may surmise that what is meant by the dictum, mitzvos are not given for enjoyment” is that there is no concrete pleasure in the act of the mitzvah. Thus it is not a violation to blow the shofar that he vowed he would not use, even if he is rightfully ecstatic in performing the mitzvah. The mitzvah of blowing is a command and a duty, not a pleasure. However, a person of a higher character will derive pleasure from the mitzvah, though its source is non-physical and not under the ban of the vow.  Also see Maharal Tiferes Yisrael (6:3) where he develops a similar idea.