I suspect the nit-picky answer would be "Some do, some don't", but in general, cessationists believe miracles still happen.
I doubt there is a common universally accepted answer to "why" cessationists don't believe in certain miracles. I'd stay away from "why" because it's not part of the question, but the answer feels too short and incomplete without it.
The best I can offer is the reason why some cessationists believe certain miracles were for the early Church only, and as a result, which miracles we believe have ceased, and a few examples of those we believe in. And because it's easy, and our Church (Fundamentalist independent Baptist) is cessationist, I'll use teachings from our own pulpit.
The strongest Scriptural evidence for Cessationism, in our understanding, comes from 1 Corinthians 13 (NIV) (
1 If I speak in the tonguesa of men and of angels, but have not love,
I am only a resounding gong or a clanging cymbal. 2 If I have the gift
of prophecy and can fathom all mysteries and all knowledge, and if I
have a faith that can move mountains, but have not love, I am nothing.
3 If I give all I possess to the poor and surrender my body to the
flames,b but have not love, I gain nothing.
4 Love is patient, love is kind. It does not envy, it does not boast,
it is not proud. 5 It is not rude, it is not self-seeking, it is not
easily angered, it keeps no record of wrongs. 6 Love does not delight
in evil but rejoices with the truth. 7 It always protects, always
trusts, always hopes, always perseveres.
8 Love never fails. But where there are prophecies, they will cease;
where there are tongues, they will be stilled; where there is
knowledge, it will pass away. 9 For we know in part and we prophesy in
part, 10 but when perfection comes, the imperfect disappears. 11 When
I was a child, I talked like a child, I thought like a child, I
reasoned like a child. When I became a man, I put childish ways behind
me. 12 Now we see but a poor reflection as in a mirror; then we shall
see face to face. Now I know in part; then I shall know fully, even as
I am fully known.
13 And now these three remain: faith, hope and love. But the greatest
of these is love.
In short, the teaching goes like this (and I'm probably butchering it by keeping it short.)
Verses 1-7 are not speaking specifically of the cessation of gifts, but instead show that the gifts are imperfect. The idea that they are not perfect gifts comes into play later in the teaching...
Verses 8 and 9 tell us that certain gifts will pass away.
Verse 10 tells us that when they will pass away - when perfection comes.
Verses 11-12 expound on the why they will pass away, and add meaning to the when - they will pass away because at some point they will be no longer needed. For this next point, it's important to note that the word used for "perfection" and "perfect" can also be translated as "mature".
While I realize this can be taken any number of ways, the general understanding in our Church is that this is speaking of the canonization of Scripture and the full understanding of God's revealed Word. In the New Testament Church, they didn't have the full Word of God. it was still being written.
Also, the signs and miracles described were always demonstrations of authority. They accompanied the Apostles as signs to show that they had the power of God, and therefore authority to instruct in His name. This is consistent with Christ's ministry, as His miracles weren't just for show - they were to establish His power and Authority. Once the Church was established, there would be no more need for these showy miracles.
As to which miracles would cease, we include the ones listed, but also, in general, tend to view Faith Healers as frauds, and reject "showy" miracles due to the implications of verse 1. The way most people present these miracles today tends to bring glory and honor to themselves, not to God.
We do believe in God's healing power. We believe He can miraculously heal the sick. We have a little girl in our Church, born with half a heart, and given a 10% chance to live that is alive and well in spite of incredible odds, and we attribute this to the power of God, responding to the fervent prayers of His people.
We believe in His ability to guide us through the Holy Spirit. We actually believe He can perform any miracle. In fact, we do believe He could and will again use prophecy and tongues. The two witnesses in Revelation - when they speak and everyone hears them in their own language, and prophesy, that will occur, and will be of God.
On that note, I'll throw in one other reason that we don't believe in speaking in tongues in particular. In the New Testament, the example is given in Acts 2:6
When they heard this sound, a crowd came together in bewilderment,
because each one heard them speaking in his own language.
This has nothing to do with the unintelligible babbling that many call "speaking in tongues" today.
Again, this is the teaching of a particular set of believers. It's not universal. Views vary.